Publications
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106 publications
Journal articles
@article{muchandimath2026_multifidelity_transport_map_coupling, author = {Muchandimath, Sanjan C. and Martins, Joaquim R. R. A. and Gorodetsky, Alex A.}, title = {Accelerating Bayesian inference via multifidelity transport map coupling}, journal = {AIAA Journal}, year = {2026}, pages = {1-17}, doi = {10.2514/1.J066460}, url = {https://arxiv.org/pdf/2510.17946} }Mathematical models in computational physics contain uncertain parameters that impact prediction accuracy. In turbulence modeling, this challenge is especially significant: Reynolds averaged Navier-Stokes (RANS) models, such as the Spalart-Allmaras (SA) model, are widely used for their speed and robustness but often suffer from inaccuracies and associated uncertainties due to imperfect model parameters. Reliable quantification of these uncertainties is becoming increasingly important in aircraft certification by analysis, where predictive credibility is critical. Bayesian inference provides a framework to estimate these parameters and quantify output uncertainty, but traditional methods are prohibitively expensive, especially when relying on high-fidelity simulations. We address the challenge of expensive Bayesian parameter estimation by developing a multi-fidelity framework that combines Markov chain Monte Carlo (MCMC) methods with multilevel Monte Carlo (MLMC) estimators to efficiently solve inverse problems. The MLMC approach requires correlated samples across different fidelity levels, achieved through a novel transport map-based coupling algorithm. We demonstrate a 50% reduction in inference cost compared to traditional single-fidelity methods on the challenging NACA0012 airfoil at high angles of attack near stall, while delivering realistic uncertainty bounds for model predictions in complex separated flow regimes. These results demonstrate that multi-fidelity approaches significantly improve turbulence parameter calibration, paving the way for more accurate and efficient aircraft certification by analysis.
@article{marks2026_generative_field_inversion, author = {Marks, Thomas A. and Gorodetsky, Alex A.}, title = {Diffusion-based probabilistic field inversion in 1-D Hall thruster simulations}, journal = {Plasma Sources Science and Technology}, year = {2026}, doi = {10.1088/1361-6595/ae8f74} }A diffusion model is used to probabilistically reconstruct the full one-dimensional state of a Hall thruster from partial, uncertain observations. The model is trained on a dataset of one-dimensional simulations of an SPT-100 thruster and sampled by iterative denoising, guided by sparse measurements. It is evaluated as a forward surrogate, where it correctly predicts the plasma density, electron temperature, and ion velocity with low uncertainty when conditioned on an input anomalous collision frequency profile. The model also matches ground-truth results from Markov chain Monte Carlo (MCMC) when conditioned on observation of the ion velocity. It additionally solves probabilistic inverse problems on real and simulated experimental data, with results that approach or match existing semi-analytic methods in quality, flexibility, and robustness to noise and missing data fields. Ablations are performed with respect to the amount of data required, the size of the model, the form of the loss function, and the number of steps taken during sampling.These highlight the large impact of dataset size on the quality of the model. Comparisons of the cost of diffusion-based inference to that of MCMC demonstrate the method's potential utility in settings requiring repeated inference, including in digital twins and model predictive control.
@article{guo2026_hierarchical_tn_structure_search, author = {Guo, Zheng and Deshpande, Aditya S. and Wang, Xinyu and Kiedrowski, Brian C. and Gorodetsky, Alex A.}, title = {Hierarchical search of tree tensor networks for high-dimensional data}, journal = {Journal of Computational Physics}, year = {2026}, volume = {566}, pages = {115230}, doi = {10.1016/j.jcp.2026.115230}, url = {https://www.sciencedirect.com/science/article/pii/S0021999126005814}, issn = {0021-9991}, keywords = {Tensor network structure search, Tensor networks, Low-rank tensor approximation, Adaptive data compression, Simulation compression} }Tensor network methods provide a scalable solution to represent high-dimensional data. However, their efficacy is often limited by static, expert-defined structures that fail to adapt to evolving data correlations. We address this limitation by formalizing the structural rounding problem for tree tensor networks and introducing a hierarchical search algorithm HiST, which automatically identifies optimized structures with index reshaping for input tree tensor networks. To navigate the combinatorial explosion of the structural search space, HiST integrates stochastic sub-network sampling with hierarchical refinement. This approach utilizes entropy-guided index clustering to reduce dimensionality and targeted reshaping to expose latent data correlations. Numerical experiments on analytical functions and real-world physics applications, including thermal radiation transport, neutron diffusion, and computational fluid dynamics, demonstrate that HiST exhibits empirical polynomial scaling with dimensionality relative to the sampling budget, bypassing the scalability barriers in prior work. HiST achieves compression ratios 2.5 × to 100 × higher than standard fixed formats such as Tensor Trains and Hierarchical Tuckers (peaking at 1000 × ). Furthermore, HiST discovers structures that generalize effectively: applying a structure optimized for one data instance to a related target data typically maintains compression performance within 10\% of the result obtained by performing structure search on that target data. These results highlight HiST as a robust, automated tool for adaptive data representation and high-dimensional simulation compression with tensor network methods.
@article{aksoy2024_incremental_hierarchical_tucker, author = {Aksoy, Doruk and Gorodetsky, Alex A.}, title = {Incremental hierarchical Tucker decomposition}, journal = {Journal of Computational Physics}, year = {2026}, url = {https://arxiv.org/pdf/2412.16544}, note = {Accepted} }We present two new algorithms for approximating and updating the hierarchical Tucker decomposition of tensor streams. The first algorithm, Batch Hierarchical Tucker - leaf to root (BHT-l2r), proposes an alternative and more efficient way of approximating a batch of similar tensors in hierarchical Tucker format. The second algorithm, Hierarchical Tucker - Rapid Incremental Subspace Expansion (HT-RISE), updates the batch hierarchical Tucker representation of an accumulated tensor as new batches of tensors become available. The HT-RISE algorithm is suitable for the online setting and never requires full storage or reconstruction of all data while providing a solution to the incremental Tucker decomposition problem. We provide theoretical guarantees for both algorithms and demonstrate their effectiveness on physical and cyber-physical data. The proposed BHT-l2r algorithm and the batch hierarchical Tucker format offers up to $6.2\\times$ compression and $3.7\\times$ reduction in time over the hierarchical Tucker format. The proposed HT-RISE algorithm also offers up to $3.1\\times$ compression and $3.2\\times$ reduction in time over a state of the art incremental tensor train decomposition algorithm.
@article{cui2026_low_rank_bayesian_matrix_completion, author = {Cui, Tiangang and Gorodetsky, Alex A.}, title = {Low-rank Bayesian matrix completion via geodesic Hamiltonian Monte Carlo on Stiefel manifolds}, journal = {Foundations of Data Science}, year = {2026}, doi = {10.3934/fods.2026015}, url = {https://arxiv.org/pdf/2410.20318} }We present a new sampling-based approach for enabling efficient computation of low-rank Bayesian matrix completion and quantifying the associated uncertainty. First, we design a new prior model based on the singular-value-decomposition (SVD) parametrization of low-rank matrices. Our prior is analogous to the seminal nuclear-norm regularization used in non-Bayesian setting and enforces orthogonality in the factor matrices by constraining them to Stiefel manifolds. Then, we design a geodesic Hamiltonian Monte Carlo (-within-Gibbs) algorithm for generating posterior samples of the SVD factor matrices. We demonstrate that our approach resolves the sampling difficulties encountered by standard Gibbs samplers for the common two-matrix factorization used in matrix completion. More importantly, the geodesic Hamiltonian sampler allows for sampling in cases with more general likelihoods than the typical Gaussian likelihood and Gaussian prior assumptions adopted in most of the existing Bayesian matrix completion literature. We demonstrate applications of our approach to fit the categorical data of a mice protein dataset and the MovieLens recommendation problem. Numerical examples demonstrate superior sampling performance, including better mixing and faster convergence to a stationary distribution. Moreover, they demonstrate improved accuracy on the two real-world benchmark problems we considered.
@article{deshpande2026_multigroup_radiation_transport_tensor_trains, author = {Deshpande, Aditya S. and Mullen, Patrick D. and Gorodetsky, Alex A. and Dolence, Joshua C. and Meyer, Chad D. and Miller, Jonah M. and Roberts, Luke F.}, title = {Multigroup thermal radiation transport with tensor trains}, journal = {The Astrophysical Journal}, year = {2026}, volume = {1003}, number = {2}, articleno = {193}, doi = {10.3847/1538-4357/ae6445} }We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally infeasible on conventional hardware. We show that solutions to certain multigroup problems possess an intrinsic low-rank structure, which the TT representation leverages effectively. This enables us to solve problems where the discretized solution size exceeds a trillion parameters on a single node. The solver is evaluated on a range of test problems with varying levels of complexity, consistently achieving compression factors greater than $100 \times$ and speedups exceeding $2 \times$. We also investigate alternative TT topologies by analyzing the low-rank structure of the merged spatio-spectral core to assess the potential for greater compression. This analysis suggests that compression gains could increase by factors as large as $7$. Our results indicate that the low-rank structure of the merged spatio-spectral core captures the spatio-spectral complexity of the solution, largely driven by the opacity structure of the medium. Beyond identifying opportunities for improved compression, this analysis highlights the types of errors that may arise in angle-integrated quantities when exploiting this low-rank structure.
@article{allen2026_optimal_experimental_design, author = {Allen, Madison and Eckels, Joshua and Gorodetsky, Alex A. and Jorns, Benjamin}, title = {Optimal experimental design for calibrating a model for the response of a Hall thruster plume to facility pressure}, journal = {Journal of Applied Physics}, year = {2026}, volume = {140}, number = {12}, pages = {123304}, month = {09}, doi = {10.1063/5.0308891}, url = {https://doi.org/10.1063/5.0308891}, issn = {0021-8979}, eprint = {https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0308891/21153249/123304_1_5.0308891.pdf} }An Optimal Experimental Design (OED) algorithm is implemented on a reduced fidelity model for the response of the plume of a Hall effect thruster to background neutral pressure with the goal of increasing the efficiency of calibrating the model against experimental data. The investigated plume model is based on a semi-analytical formulation that accounts for collisional effects. A previously published dataset from the SPT-100 Hall thruster of current density and ion energy as a function of position and background pressure is employed as a test case. Both myopic and myopic with batches OED methods are explored for identifying subsets of measurements from the dataset for rapid model calibration. It is found that both methods are able to achieve the same confidence in model parameter inference as a calibration performed with the full dataset but with approximately 60\% of the measurements. This result is discussed in the context of best practices for designing future experimental campaigns to evaluate facility effects in Hall thrusters.
@article{dixon2026_automate_multifidelity_statistical_estimation, author = {Dixon, Thomas O. and Gorodetsky, Alex A. and Jakeman, John D. and Narayan, Akil and Xu, Yiming}, title = {Optimally balancing exploration and exploitation to automate multi-fidelity statistical estimation}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, year = {2026}, doi = {10.1137/25M1761744}, url = {https://arxiv.org/pdf/2505.09828} }Abstract.Multifidelity methods that use an ensemble of models to compute a Monte Carlo estimator of the expectation of a high-fidelity model can significantly reduce computational costs compared to single-model approaches. These methods use oracle statistics, specifically the covariance between models, to optimally allocate samples to each model in the ensemble. However, in practice, the oracle statistics are estimated using additional model evaluations, whose computational cost and induced error are typically ignored. To address this issue, this paper proposes an adaptive algorithm to optimally balance the resources between oracle statistics estimation and final multifidelity estimator construction, leveraging ideas from multilevel best linear unbiased estimators in Schaden and Ullmann (SIAM/ASA J. Uncertain. Quantif., 8 (2020), pp. 601–635) and a bandit-learning procedure in Xu et al. (SIAM J. Sci. Comput., 44 (2022), pp. A150–A175). Under mild assumptions, we demonstrate that the multifidelity estimator produced by the proposed algorithm exhibits mean-squared error commensurate with that of the best linear unbiased estimator under the optimal allocation computed with oracle statistics. Our theoretical findings are supported by detailed numerical experiments, including a parametric elliptic PDE and an ice-sheet mass-change modeling problem.
@article{wang2026_sequential_variational_framework, author = {Wang, Liliang and Gorodetsky, Alex A.}, title = {Sequential Bayesian parameter-state estimation in dynamical systems with noisy and incomplete observations via a variational framework}, journal = {Journal of Computational Physics}, year = {2026}, volume = {563}, articleno = {115057}, doi = {10.1016/j.jcp.2026.115057} }Online joint estimation of a dynamical model's unknown parameters and states with uncertainty quantification is crucial in many applications. For example, digital twins dynamically update their knowledge of model parameters and states to support prediction and decision-making. Reliability and computational speed are vital for digital twins. Online parameter-state estimation ensures computational efficiency, while uncertainty quantification is essential for making reliable predictions and decisions. In parameter-state estimation, the joint distribution of the state and model parameters conditioned on the data, termed the joint posterior, provides accurate uncertainty quantification. Because the joint posterior is generally intractable to compute, this paper presents an online variational inference framework to compute its approximation at each time step. The approximation is factorized into a marginal distribution over the model parameters and a state distribution conditioned on the parameters. This factorization enables recursive updates through a two-stage procedure: first, the parameter posterior is approximated via variational inference; second, the state distribution conditioned on the parameters is computed using Gaussian filtering based on the approximate parameter posterior. The algorithmic design is supported by a theorem establishing upper bounds on the joint posterior approximation error. Numerical experiments demonstrate that the proposed method (i) accurately infers both unobserved states and unknown parameters of dynamical and observation models; (ii) remains robust under noisy, partial observations and model discrepancies in a chaotic Lorenz 96 system; and (iii) scales effectively to a high-dimensional state-space system arising from the spatial discretization of a convection-diffusion equation, outperforming the joint ensemble Kalman filter in this setting.
@article{lipscomb2026_vacuum_chamber_pressure_uq, author = {Lipscomb, Charles P. and Boyd, Iain D. and Hansson, Kaelan B. and Eckels, Joshua D. and Gorodetsky, Alex A.}, title = {Simulation of vacuum chamber pressure distributions with uncertainty quantification}, journal = {Journal of Propulsion and Power}, year = {2026}, volume = {42}, number = {2}, pages = {256-266}, doi = {10.2514/1.B39954} }One of the primary challenges in understanding variations in electric propulsion performance between ground tests and space operations lies in the pressure distribution within the test vacuum chamber. The chamber backpressure is much higher than experienced in space, modifying thruster performance and plume dynamics. Numerical simulation is a key element in determining the background conditions in nonideal vacuum chamber environments. An important parameter for the accurate simulation of chamber backpressure is the sticking coefficient, which sets the probability that an atom will stick to a cryogenic panel used to pump away the plume gases. This quantity can be used to model vacuum pumps in particle-based kinetic numerical methods. In this work, a three-dimensional direct simulation Monte Carlo code is used to model neutral xenon atoms flowing from the anode of the H9 Hall effect thruster within a large vacuum test facility. Simulated pressures are compared with ion gauge pressure measurements to infer the effective sticking coefficient of the chamber's vacuum pumps. A pressure-predicting surrogate model is developed for inference of pump sticking coefficients and for uncertainty quantification. This information facilitates accurate and useful kinetic simulations of electric propulsion thruster plasma plumes in vacuum chambers.
@article{pickard2025_brad_biomarkers, author = {Pickard, Joshua and Prakash, Ram and Choi, Marc Andrew and Oliven, Natalie and Stansbury, Cooper and Cwycyshyn, Jillian and Galioto, Nicholas and Gorodetsky, Alex A. and Velasquez, Alvaro and Rajapakse, Indika}, title = {Automatic biomarker discovery and enrichment with BRAD}, journal = {Bioinformatics}, year = {2025}, volume = {41}, number = {5}, articleno = {btaf159}, doi = {10.1093/bioinformatics/btaf159} }Motivation: Integrating large language models with research tools presents technical and reproducibility challenges for biomedical research. While commercial artificial intelligence systems are easy to adopt, they obscure data provenance, lack transparency, and can generate false information, making them unfit for many research problems. To address these challenges, we developed the Bioinformatics Retrieval Augmented Digital agent software system. Results: We introduce BRAD, an agentic system that integrates large language models with external tools and data to streamline research workflows. BRAD's modular agents retrieve information from literature, custom software, and online databases while maintaining transparent protocols to increase the reliability of AI-generated results. We apply BRAD to a biomarker discovery pipeline, automating both execution and the generation of enrichment reports. This workflow contextualizes user data within the literature, enabling a level of interpretation and automation that surpasses conventional research tools. Beyond the workflow highlighted here, BRAD is a flexible system that has been deployed in other applications including a chatbot, video retrieval-augmented generation, and analysis of single-cell data. Availability and implementation: The source code for BRAD is available at https://github.com/Jpickard1/BRAD; information for pip installation, tutorials, documentation, and further information can be found at ReadTheDocs.
@article{zeng2025_basis_adaptation_bmfnets, author = {Zeng, Xiaoshu and Geraci, Gianluca and Gorodetsky, Alex A. and Jakeman, John D. and Ghanem, Roger G.}, title = {Boosting efficiency and reducing graph reliance: Basis adaptation integration in Bayesian multi-fidelity networks}, journal = {Computer Methods in Applied Mechanics and Engineering}, year = {2025}, volume = {436}, articleno = {117657}, doi = {10.1016/j.cma.2024.117657}, keywords = {Surrogate models; Multi-fidelity methods; Dimension reduction; Uncertainty quantification} }The computational cost of high-fidelity numerical models makes outer-loop analysis, which requires repeated interrogation of the model such as uncertainty quantification, computationally demanding. Multi-fidelity methods, which construct a surrogate model using data from an ensemble of models of varying cost and accuracy, can substantially reduce the cost of outer-loop analysis. However, these methods can be difficult to apply when the model ensemble does not admit a clear hierarchy a priori and the correlations between models are low. Consequently, in this paper, we present a multi-fidelity method that leverages dimension reduction to enhance the correlation between models, thereby reducing the amount of data needed to train a surrogate from an unordered ensemble of models. Our method utilizes basis adaptation to build low-dimensional polynomial chaos expansions of each model and employs Multi-fidelity Networks to encode the relationships among models. We show that the resulting method exhibit two notable advantages over its counterpart: (1) enhanced accuracy (both reduced bias and variance); and (2) reduced dependency on the graph structure encoding relationships among models. We demonstrate the approach on an analytical test problem and a challenging finite element model for a spent nuclear fuel. Our method produces a surrogate model that is significantly more accurate than either a single-fidelity surrogate or a multi-fidelity surrogate constructed without basis adaptation.
@article{marks2025_warpx_hall_thruster, author = {Marks, Thomas A. and Gorodetsky, Alex A.}, title = {GPU-accelerated kinetic Hall thruster simulations in WarpX}, journal = {Journal of Electric Propulsion}, year = {2025}, volume = {4}, number = {1}, articleno = {34}, doi = {10.1007/s44205-025-00133-1} }Two-dimensional axial-azimuthal simulations of a Hall thruster are performed using the open-source particle-in-cell code WarpX. The simulation conditions are chosen to match those of the axial-azimuthal benchmark first reported by Charoy et al. in 2019. A range of numerical and solver parameters is investigated in order to find those which yield the best performance. It is found that WarpX completes the benchmark case in 3.8 days on an Nvidia V100 GPU, and in as low as 1.5 days on a more recent Nvidia H100 GPU. Of the numerical parameters investigated, it is determined that the field-solve tolerance and particle resampling thresholds have the largest effect on the simulation wall time and that particle resampling may artificially widen electron velocity distribution functions, leading to unphysical heating. A semi-implicit scheme for the electrostatic field solve is tested and is found to produce results consistent to within 10% of the benchmark in less than twelve hours. The scaling properties of the electrostatic solver to multiple GPUs are also assessed on a uniform plasma test problem. The results of this work are discussed in the context of advancements in GPU hardware and the suitability of kinetic Hall thruster simulations for engineering applications.
@article{dixon2025_satellite_pose_uncertainty, author = {Dixon, Thomas O. and Giles, Stephen A. and Gorodetsky, Alex A.}, title = {Predicting uncertainty in vision-based satellite pose estimation using deep evidential regression}, journal = {Aerospace Science and Technology}, year = {2025}, volume = {160}, articleno = {110055}, doi = {10.1016/j.ast.2025.110055}, url = {https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4977769} }In this work, we demonstrate the use of evidential regression to quantify uncertainty in satellite pose estimation within vision-based deep-learning models trained on images of the Tango satellite. Our approach augments existing deep-learning models with uncertainty prediction capability using evidential regression. We show that the resulting uncertainty is well correlated with prediction errors, while maintaining comparable pointwise-prediction accuracies to existing models. Leveraging evidential regression to predict epistemic and aleatoric uncertainties, we demonstrate a median 0.996 correlation between network prediction error and these uncertainty estimates on keypoint coordinates within synthetic images. Additionally, we demonstrate that predicting on out-of-distribution images as well as increasing image noise directly amplifies uncertainty in pose estimation. By validating our framework's ability to quantify uncertainty, we enable robust decision-making in risky satellite operations.
@article{gorodetsky2025_thermal_radiation_transport_tensor_trains, author = {Gorodetsky, Alex A. and Mullen, Patrick D. and Deshpande, Aditya S. and Dolence, Joshua C. and Meyer, Chad D. and Miller, Jonah M. and Roberts, Luke F.}, title = {Thermal radiation transport with tensor trains}, journal = {The Astrophysical Journal}, year = {2025}, volume = {988}, number = {1}, articleno = {64}, doi = {10.3847/1538-4357/adda3f} }We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train decomposition for the specific intensity. The efficiency of this approach is dictated by the rank of the decomposition. When the solution is low rank, the memory footprint of the specific intensity solution vector may be significantly compressed. The algorithm, following a step-then-truncate approach of a traditional discrete ordinates method, operates directly on the compressed state vector, thereby enabling large speedups for low-rank solutions. To achieve these speedups, we rely on a recently developed rounding approach based on the Gram-SVD. We detail how familiar SN algorithms for gray thermal transport can be mapped to this tensor train framework and present several numerical examples testing both the optically thick and thin regimes. The tensor train framework finds low-rank structure and supplies up to 60x speedups and 1000x compressions for problems demanding large angle counts, thereby enabling previously intractable SN calculations and supplying a promising avenue to mitigate ray effects.
@article{marks2025_multicomponent_hall_thruster_uq, author = {Marks, Thomas A. and Eckels, Joshua D. and Mora, Gabriel E. and Gorodetsky, Alex A.}, title = {Uncertainty quantification of a multi-component Hall thruster model at varying facility pressures}, journal = {Journal of Applied Physics}, year = {2025}, volume = {138}, number = {15}, articleno = {153305}, doi = {10.1063/5.0283796} }Bayesian inference is applied to calibrate and quantify prediction uncertainty in a coupled multi-component Hall thruster model. The model consists of cathode, discharge, and plume sub-models and outputs thruster performance metrics, one-dimensional plasma properties, and the angular distribution of the current density in the plume. The simulated thrusters include a magnetically shielded thruster operating on krypton, the H9, and an unshielded thruster operating on xenon, the SPT-100, at pressures between 4.3--43 $\mu$Torr-Kr and 1.7--80 $\mu$Torr-Xe, respectively. After calibration, the model captures key pressure-related trends, including changes in thrust and upstream shifts in the ion acceleration region. Furthermore, the model exhibits predictive accuracy to within 10\% when evaluated on flow rates and pressures not included in the training data, and can predict some performance characteristics across test facilities to within the same range of conditions. Compared to a previous model calibrated on some of the same data [Eckels et al. 2024], the model reduced predictive errors in thrust and discharge current by greater than 50\%. An extrapolation to on-orbit performance is performed with an error of 9\%, capturing trends in discharge current but not thrust. These findings are discussed in the context of using data for predictive Hall thruster modeling in the presence of facility effects.
@article{aksoy2024_incremental_tensor_train, author = {Aksoy, Doruk and Gorsich, David J. and Veerapaneni, Shravan and Gorodetsky, Alex A.}, title = {An incremental tensor train decomposition algorithm}, journal = {SIAM Journal on Scientific Computing}, year = {2024}, volume = {46}, number = {2}, pages = {A1047-A1075}, doi = {10.1137/22M1537734}, url = {https://arxiv.org/pdf/2211.12487} }We present a new algorithm for incrementally updating the tensor train decomposition of a stream of tensor data. This new algorithm, called the tensor train incremental core expansion (TT-ICE), improves upon the current state-of-the-art algorithms for compressing in tensor train format by developing a new adaptive approach that incurs significantly slower rank growth and guarantees compression accuracy. This capability is achieved by limiting the number of new vectors appended to the TT-cores of an existing accumulation tensor after each data increment. These vectors represent directions orthogonal to the span of existing cores and are limited to those needed to represent a newly arrived tensor to a target accuracy. We provide two versions of the algorithm: TT-ICE and TT-ICE accelerated with heuristics (TT-ICE*). We provide a proof of correctness for TT-ICE and empirically demonstrate the performance of the algorithms in compressing large-scale video and scientific simulation datasets. Compared to existing approaches that also use rank adaptation, TT-ICE* achieves 57x higher compression and up to 95\% reduction in computational time.
@article{galioto2024_nonseparable_hamiltonians, author = {Galioto, Nicholas and Sharma, Harsh and Kramer, Boris and Gorodetsky, Alex A.}, title = {Bayesian identification of nonseparable Hamiltonians with multiplicative noise using deep learning and reduced-order modeling}, journal = {Computer Methods in Applied Mechanics and Engineering}, year = {2024}, volume = {430}, articleno = {117194}, doi = {10.1016/j.cma.2024.117194}, url = {https://arxiv.org/pdf/2401.12476} }This paper presents a structure-preserving Bayesian approach for learning nonseparable Hamiltonian systems using stochastic dynamic models allowing for statistically-dependent, vector-valued additive and multiplicative measurement noise. The approach is comprised of three main facets. First, we derive a Gaussian filter for a statistically-dependent, vector-valued, additive and multiplicative noise model that is needed to evaluate the likelihood within the Bayesian posterior. Second, we develop a novel algorithm for cost-effective application of Bayesian system identification to high-dimensional systems. Third, we demonstrate how structure-preserving methods can be incorporated into the proposed framework, using nonseparable Hamiltonians as an illustrative system class. We assess the method's performance based on the forecasting accuracy of a model estimated from single-trajectory data. We compare the Bayesian method to a state-of-the-art machine learning method on a canonical nonseparable Hamiltonian model and a chaotic double pendulum model with small, noisy training datasets. The results show that using the Bayesian posterior as a training objective can yield upwards of 724 times improvement in Hamiltonian mean squared error using training data with up to 10\% multiplicative noise compared to a standard training objective. Lastly, we demonstrate the utility of the novel algorithm for parameter estimation of a 64-dimensional model of the spatially discretized nonlinear Schr\odinger equation with data corrupted by up to 20\% multiplicative noise.
@article{dixon2024_acv_covariance_expressions, author = {Dixon, Thomas O. and Warner, James E. and Bomarito, Geoffrey F. and Gorodetsky, Alex A.}, title = {Covariance expressions for multifidelity sampling with multioutput, multistatistic estimators: application to approximate control variates}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, year = {2024}, volume = {12}, number = {3}, pages = {1005-1049}, doi = {10.1137/23M1607994}, url = {https://arxiv.org/pdf/2310.00125} }We provide a collection of results on covariance expressions between Monte Carlo based multi-output mean, variance, and Sobol main effect variance estimators from an ensemble of models. These covariances can be used within multi-fidelity uncertainty quantification strategies that seek to reduce the estimator variance of high-fidelity Monte Carlo estimators with an ensemble of low-fidelity models. Such covariance expressions are required within approaches like the approximate control variate and multi-level best linear unbiased estimator. While the literature provides these expressions for some single-output cases such as mean and variance, our results are relevant to both multiple function outputs and multiple statistics across any sampling strategy. Following the description of these results, we use them within an approximate control variate scheme to show that leveraging multiple outputs can dramatically reduce estimator variance compared to single-output approaches. Synthetic examples are used to highlight the effects of optimal sample allocation and pilot sample estimation. A flight-trajectory simulation of entry, descent, and landing is used to demonstrate multi-output estimation in practical applications.
@article{eckels2024_hall_thruster_model_improvement, author = {Eckels, Joshua D. and Marks, Thomas A. and Allen, Madison G. and Jorns, Benjamin A. and Gorodetsky, Alex A.}, title = {Hall thruster model improvement by multidisciplinary uncertainty quantification}, journal = {Journal of Electric Propulsion}, year = {2024}, volume = {3}, number = {1}, articleno = {19}, doi = {10.1007/s44205-024-00079-w} }We study the analysis and refinement of a predictive engineering model for enabling rapid prediction of Hall thruster system performance across a range of operating and environmental conditions and epistemic and aleatoric uncertainties. In particular, we describe an approach by which experimentally observed facility effects are assimilated into the model, with a specific focus on facility background pressure. We propose a multifidelity, multidisciplinary approach for Bayesian calibration of an integrated system comprised of a set of component models. Furthermore, we perform uncertainty quantification over the calibrated model to assess the effects of epistemic and aleatoric uncertainty. This approach is realized on a coupled system of cathode, thruster, and plume models that predicts global quantities of interest such as thrust, efficiency, and discharge current as a function of operating conditions such as discharge voltage, mass flow rate, and background chamber pressure. As part of the calibration and prediction, we propose a number of metrics for assessing predictive model quality. Based on these metrics, we found that our proposed framework produces a calibrated model that is more accurate, sometimes by an order of magnitude, than engineering models using nominal parameters found in the literature. We also found for many quantities of interest that the remaining uncertainty was not sufficient to account for discrepancy with experimental data, and that existing models for facility effects do not sufficiently capture experimental trends. Finally, we confirmed through a global sensitivity analysis the prior intuition that anomalous transport dominates model uncertainty, and we conclude by suggesting several paths for future model improvement. We envision that the proposed metrics and procedures can guide the refinement of future model development activities.
@article{galioto2024_likelihood_based_system_identification, author = {Galioto, Nicholas and Gorodetsky, Alex A.}, title = {Likelihood-based generalization of Markov parameter estimation and multiple shooting objectives in system identification}, journal = {Physica D: Nonlinear Phenomena}, year = {2024}, volume = {462}, articleno = {134146}, doi = {10.1016/j.physd.2024.134146}, url = {https://arxiv.org/pdf/2212.13902} }This paper considers the problem of system identification (ID) of linear and nonlinear non-autonomous systems from noisy and sparse data. We propose and analyze an objective function derived from a Bayesian formulation for learning a hidden Markov model with stochastic dynamics. We then analyze this objective function in the context of several state-of-the-art approaches for both linear and nonlinear system ID. In the former, we analyze least squares approaches for Markov parameter estimation, and in the latter, we analyze the multiple shooting approach. We demonstrate the limitations of the optimization problems posed by these existing methods by showing that they can be seen as special cases of the proposed optimization objective under certain simplifying assumptions: conditional independence of data and zero model error. Furthermore, we observe that our proposed approach has improved smoothness and inherent regularization that make it well-suited for system ID and provide mathematical explanations for these characteristics' origins. Finally, numerical simulations demonstrate a mean squared error over 8.7 times lower compared to multiple shooting when data are noisy and/or sparse. Moreover, the proposed approach can identify accurate and generalizable models even when there are more parameters than data or when the underlying system exhibits chaotic behavior.
@article{chen2024_low_rank_tensor_network_behavioral_cloning, author = {Chen, Brian and Aksoy, Doruk and Gorsich, David J. and Veerapaneni, Shravan and Gorodetsky, Alex A.}, title = {Low-rank tensor-network encodings for video-to-action behavioral cloning}, journal = {Transactions on Machine Learning Research}, year = {2024}, url = {https://openreview.net/pdf?id=w4DXLzBPPw} }We describe a tensor-network latent-space encoding approach for increasing the scalability of behavioral cloning of a video game player's actions entirely from video streams of the gameplay. Specifically, we address challenges associated with the high computational requirements of traditional deep-learning based encoders such as convolutional variational autoencoders that prohibit their use in widely available hardware or for large scale data. Our approach uses tensor networks instead of deep variational autoencoders for this purpose, and it yields significant speedups with no loss of accuracy. Empirical results on ATARI games demonstrate that our approach leads to a speedup in the time it takes to encode data and train a predictor using the encodings (between 2.6x to 9.6x compared to autoencoders or variational autoencoders). Furthermore, the tensor train encoding can be efficiently trained on CPU to achieve comparable or better training times than the autoencoder and variational autoencoder trained on GPU (0.9x to 5.4x faster). These results suggest significant possibilities in mitigating the need for cost and time-intensive hardware for training deep-learning architectures for behavioral cloning.
@article{yang2023_control_variate_polynomial_chaos, author = {Yang, Hang and Fujii, Yuji and Wang, Kon-Well and Gorodetsky, Alex A.}, title = {Control variate polynomial chaos: optimal fusion of sampling and surrogates for multifidelity uncertainty quantification}, journal = {International Journal of Uncertainty Quantification}, year = {2023}, volume = {13}, number = {3}, pages = {69-100}, doi = {10.1615/Int.J.UncertaintyQuantification.2022043638}, url = {https://arxiv.org/pdf/2201.10745.pdf} }We present a multifidelity uncertainty quantification numerical method that leverages the benefits of both sampling and surrogate modeling, while mitigating their downsides, for enabling rapid computation in complex dynamical systems such as automotive propulsion systems. In particular, the proposed method utilizes intrusive generalized polynomial chaos to quickly generate additional information that is highly correlated with the original nonlinear dynamical system. We then leverage a Monte Carlo-based control variate to correct the bias caused by the surrogate approximation. In contrast to related works merging adaptive surrogate approximation and sampling in a multifidelity setting, the intrusive generalized polynomial chaos surrogate is selected because it avoids statistical errors by design by providing analytical estimates of output statistics. Moreover, it enables theoretical contributions that provide an estimator design strategy that optimally balances the computational efforts allocated to sampling and to generalized polynomial chaos construction. We deploy our approach to multiple numerical examples including simulations of hybrid-electric propulsion systems, where the proposed estimator is shown to achieve orders-of-magnitude reduction in mean squared error of statistics estimation under comparable costs of purely sampling or purely surrogate approaches.
@article{salehi2023_tensor_review_civil, author = {Salehi, Hadi and Gorodetsky, Alex A. and Solhmirzaei, Roya and Jiao, Pengcheng}, title = {High-dimensional data analytics in civil engineering: a review on matrix and tensor decomposition}, journal = {Engineering Applications of Artificial Intelligence}, year = {2023}, volume = {125}, articleno = {106659}, doi = {10.1016/j.engappai.2023.106659} }Recent developments in sensing and monitoring techniques have led to the generation of high-dimensional data in the field of civil engineering. High-dimensional data analytics methods have thus been developed to interpret such complex data. Among the different high-dimensional data analytics techniques, matrix and tensor decomposition methods have acquired a notable interest in the civil engineering community over the past decade. Due to their unique ability to deal with highly redundant and correlated data, these methods are establishing themselves as promising and efficient tools to analyze high-dimensional data in the civil engineering arena. In this paper, high-dimensional data is referred to as a data set in which the number of features is comparable or larger than the number of observations. This review paper aims to summarize the applications of matrix and tensor decomposition methods in civil engineering over the last decade. The survey begins with a general overview of matrix and tensor decomposition followed by highlighting their significance in the field. Afterward, various applications of these high-dimensional data analytics methods in civil engineering are presented, while the advantages offered by these methods are discussed. Finally, challenges and potential research avenues for employing matrix and tensor decomposition and future emerging trends for their novel use are highlighted.
@article{zeng2023_dissimilar_parameters_multifidelity, author = {Zeng, Xiaoshu and Geraci, Gianluca and Eldred, Michael S. and Jakeman, John D. and Gorodetsky, Alex A. and Ghanem, Roger G.}, title = {Multifidelity uncertainty quantification with models based on dissimilar parameters}, journal = {Computer Methods in Applied Mechanics and Engineering}, year = {2023}, volume = {415}, articleno = {116205}, doi = {10.1016/j.cma.2023.116205}, url = {https://arxiv.org/pdf/2304.08644} }Multifidelity uncertainty quantification (MF UQ) sampling approaches have been shown to significantly reduce the variance of statistical estimators while preserving the bias of the highest-fidelity model, provided that the low-fidelity models are well correlated. However, maintaining a high level of correlation can be challenging, especially when models depend on different input uncertain parameters, which drastically reduces the correlation. Existing MF UQ approaches do not adequately address this issue. In this work, we propose a new sampling strategy that exploits a shared space to improve the correlation among models with dissimilar parametrization. We achieve this by transforming the original coordinates onto an auxiliary manifold using the adaptive basis (AB) method. The AB method has two main benefits: (1) it provides an effective tool to identify the low-dimensional manifold on which each model can be represented, and (2) it enables easy transformation of polynomial chaos representations from high- to low-dimensional spaces. This latter feature is used to identify a shared manifold among models without requiring additional evaluations. We present two algorithmic flavors of the new estimator to cover different analysis scenarios, including those with legacy and non-legacy high-fidelity data. We provide numerical results for analytical examples, a direct field acoustic test, and a finite element model of a nuclear fuel assembly. For all examples, we compare the proposed strategy against both single-fidelity and MF estimators based on the original model parametrization.
@article{yang2022_automotive_propulsion_multifidelity, author = {Yang, Hang and Gorodetsky, Alex A. and Fujii, Yuji and Wang, Kon-Well}, title = {A polynomial-chaos-based multifidelity approach to the efficient uncertainty quantification of online simulations of automotive propulsion systems}, journal = {Journal of Computational and Nonlinear Dynamics}, year = {2022}, volume = {17}, number = {5}, articleno = {051012}, doi = {10.1115/1.4053559} }As a result of increasing system complexity and stricter performance requirements, intelligent and robust decision-making and control capabilities are of great importance for future automotive propulsion systems. Due to uncertainties from both unavoidable modeling errors and probabilistic environmental disturbances, the ability to quantify the effect of these uncertainties on system behaviors plays a crucial role in enabling advanced control designs for propulsion systems. However, quantifying uncertainties in complex nonlinear systems can cause significant computational burdens. Given the limited computing power on-board a vehicle, developing algorithms with high enough efficiency to quantify uncertainties in automotive propulsion systems in real time is a major challenge. Traditional uncertainty quantification methods for complicated nonlinear systems, such as Monte Carlo, often rely on sampling, a computationally prohibitive process in many applications. Previous research has shown promise in using spectral decomposition methods such as generalized polynomial chaos to reduce the online computational cost of uncertainty quantification, but such methods suffer from poor scalability and bias issues. In this article, we seek to alleviate these computational bottlenecks by using a multifidelity approach that utilizes control variates to combine generalized polynomial chaos with Monte Carlo. Results on the mean, variance, and skewness estimations of vehicle axle shaft torque show that the proposed method corrects the bias caused by polynomial chaos expansions while significantly reducing the overall estimator variance compared to that of a conventional Monte Carlo estimator.
@article{jakeman2022_adaptive_experimental_design_multifidelity, author = {Jakeman, John D. and Friedman, Sam and Eldred, Michael S. and Tamellini, Lorenzo and Gorodetsky, Alex A. and Allaire, Douglas}, title = {Adaptive experimental design for multi-fidelity surrogate modeling of multi-disciplinary systems}, journal = {International Journal for Numerical Methods in Engineering}, year = {2022}, volume = {123}, number = {12}, pages = {2760-2790}, doi = {10.1002/nme.6958} }We present an adaptive algorithm for constructing surrogate models of multi-disciplinary systems composed of a set of coupled components. With this goal we introduce coupling variables with a priori unknown distributions that allow surrogates of each component to be built independently. Once built, the surrogates of the components are combined to form an integrated-surrogate that can be used to predict system-level quantities of interest at a fraction of the cost of the original model. The error in the integrated-surrogate is greedily minimized using an experimental design procedure that allocates the amount of training data, used to construct each component-surrogate, based on the contribution of those surrogates to the error of the integrated-surrogate. The multi-fidelity procedure presented is a generalization of multi-index stochastic collocation that can leverage ensembles of models of varying cost and accuracy, for one or more components, to reduce the computational cost of constructing the integrated-surrogate. Extensive numerical results demonstrate that, for a fixed computational budget, our algorithm is able to produce surrogates that are orders of magnitude more accurate than methods that treat the integrated system as a black-box.
@article{kachar2022_discrete_optimal_transport, author = {Kachar, Koray G. and Gorodetsky, Alex A.}, title = {Dynamic multi-agent assignment via discrete optimal transport}, journal = {IEEE Transactions on Control of Network Systems}, year = {2022}, volume = {9}, number = {1}, pages = {151-162}, doi = {10.1109/TCNS.2022.3141024}, url = {https://arxiv.org/abs/1910.10748} }We propose an optimal solution to a dynamic assignment problem to assign a group of moving agents to another group of moving targets. Our approach leverages connections to the theory of discrete optimal transport to convert the problem into a tractable linear program. We simultaneously solve for the optimal assignment and the control of the individual agents. As a result, we can account for dynamics and capabilities of a heterogeneous set of agents and targets. In contrast to existing assignment schemes, this approach considers cost metrics informed by the underlying agent dynamics and capabilities rather than just distance. We show that the minimizer of the dynamic assignment problem is equivalent to the minimizer of the associated Monge problem from optimal transport. We prove that the resulting approach only requires a single assignment computation over the operating lifetime, rather than periodic reassignment. Furthermore, we demonstrate cost benefits that increase as the network size increases, achieving almost 50\% cost reduction compared with distance-based metrics. We demonstrate our approach through simulation on several multi-agent and multi-target tracking problems.
@article{pham2022_ensemble_approximate_control_variates, author = {Pham, Trung and Gorodetsky, Alex A.}, title = {Ensemble approximate control variate estimators: applications to multi-fidelity importance sampling}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, year = {2022}, volume = {10}, number = {3}, pages = {1250-1292}, doi = {10.1137/21M1390426} }The recent growth in multi-fidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a high-fidelity model. In this paper we provide two contributions: (1) we utilize an ensemble estimator to account for uncertainties in the optimal weights of approximate control variate (ACV) approaches and derive lower bounds on the number of samples required to guarantee variance reduction; and (2) we extend an existing multi-fidelity importance sampling (MFIS) scheme to leverage control variates. As such we make significant progress towards both increasing the practicality of approximate control variates, for instance by accounting for the effect of pilot samples, and using multi-fidelity approaches more effectively for estimating low-probability events. The numerical results indicate our hybrid MFIS-ACV estimator achieves up to 50\% improvement in variance reduction over the existing state-of-the-art MFIS estimator, which had already shown outstanding convergence rate compared to the Monte Carlo method, on several problems of computational mechanics.
@article{soley2022_functional_tt_chebyshev, author = {Soley, Micheline B. and Bergold, Paul and Gorodetsky, Alex A. and Batista, Victor S.}, title = {Functional tensor-train Chebyshev method for multidimensional quantum dynamics simulations}, journal = {Journal of Chemical Theory and Computation}, year = {2022}, volume = {18}, number = {1}, pages = {25-36}, doi = {10.1021/acs.jctc.1c00941} }Methods for efficient simulations of multidimensional quantum dynamics are essential for theoretical studies of chemical systems where quantum effects are important, such as those involving rearrangements of protons or electronic configurations. Here, we introduce the functional tensor-train Chebyshev (FTTC) method for rigorous nuclear quantum dynamics simulations. FTTC is essentially the Chebyshev propagation scheme applied to the initial state represented in a continuous analogue tensor-train format. We demonstrate the capabilities of FTTC as applied to simulations of proton quantum dynamics in a 50-dimensional model of hydrogen-bonded DNA base pairs.
@article{aksoy2022_self_oscillatory_gels, author = {Aksoy, Doruk and Alben, Silas and Deegan, Robert D. and Gorodetsky, Alex A.}, title = {Inverse design of self-oscillatory gels through deep learning}, journal = {Neural Computing and Applications}, year = {2022}, volume = {34}, number = {9}, pages = {6879-6905}, doi = {10.1007/s00521-021-06788-9} }We develop a deep learning architecture for inverse design of a self-oscillating sheet propelled by an embedded chemical reaction. The dynamics of our problems are nonlinear and exhibit chaotic behavior, a challenging setting for existing deep-learning-based inverse-design approaches. The aim is to explore data-driven design of soft robots using a novel locomotion mechanism. We train the architecture using a forward model of the locomotion mechanism developed recently by Alben et al. (2019). The architecture is shown to successfully map a snapshot of target motions of the gel into geometric and reaction parameters. The final architecture consists of a multi-layer perceptron (MLP) classifier for discrete parameters followed by a stacked MLP regressor (SMLPR) for continuous parameters. Our inverse-design setting is unique in that it considers both discrete and continuous outputs, requiring an architecture capable of classification and regression. We are able to recover parameters within 2.87\% accuracy. We also compare the simulated motion of the sheets at the recovered parameters. Because the motion has a chaotic quality, our demonstration is able to show quantitative agreement for a small time horizon and qualitative agreement over longer time horizons. We also demonstrate agreement of Lyapunov exponents up to 6.78\% accuracy for suitable motions.
@article{gorodetsky2022_reverse_mode_tensor_networks, author = {Gorodetsky, Alex A. and Safta, Cosmin and Jakeman, John D.}, title = {Reverse-mode differentiation in arbitrary tensor network format: with application to supervised learning}, journal = {Journal of Machine Learning Research}, year = {2022}, url = {https://www.jmlr.org/papers/volume23/21-0225/21-0225.pdf} }This paper describes an efficient reverse-mode differentiation algorithm for contraction operations of tensor networks that may have arbitrary and unconventional network topologies. The approach leverages the tensor contraction tree of Evenbly and Pfeifer (2014), which provides an instruction set for the contraction sequence of a network. We show that this tree can be efficiently leveraged for differentiation of a full tensor network contraction using a recursive scheme that exploits (1) the bilinear property of contraction and (2) the property that trees have single path from root to leaves. While differentiation of tensor-tensor contraction is already possible in most automatic differentiation packages, we show that exploiting these two additional properties in the specific context of contraction sequences can improve efficiency. Following a description of the algorithm and computational complexity analysis, we investigate its utility for gradient-based supervised learning for low-rank function recovery and for fitting real-world unstructured datasets. We demonstrate improved performance over alternating least-squares optimization approaches and the capability to handle heterogeneous and arbitrary tensor network formats. When compared to alternating minimization algorithms, we find that the gradient-based approach requires a smaller oversampling ratio (number of samples compared to number of model parameters) for recovery. This increased efficiency extends to fitting unstructured data of varying dimensionality and when employing a variety of tensor network formats. Here, we show improved learning using the hierarchical Tucker method over the tensor-train in high-dimensional settings on a number of benchmark problems.
@article{gorodetsky2021_mfnets_all_at_once, author = {Gorodetsky, Alex A. and Jakeman, John D. and Geraci, Gianluca}, title = {MFNets: data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources}, journal = {Computational Mechanics}, year = {2021}, volume = {68}, number = {4}, pages = {741-758}, doi = {10.1007/s00466-021-02042-0}, url = {http://arxiv.org/abs/2008.02672} }We present an approach for constructing a surrogate from ensembles of information sources of varying cost and accuracy. The multifidelity surrogate encodes connections between information sources as a directed acyclic graph, and is trained via gradient-based minimization of a nonlinear least squares objective. While the vast majority of state-of-the-art assumes hierarchical connections between information sources, our approach works with flexibly structured information sources that may not admit a strict hierarchy. The formulation has two advantages: (1) increased data efficiency due to parsimonious multifidelity networks that can be tailored to the application; and (2) no constraints on the training data -- we can combine noisy, non-nested evaluations of the information sources. Numerical examples ranging from synthetic to physics-based computational mechanics simulations indicate the error in our approach can be orders-of-magnitude smaller, particularly in the low-data regime, than single-fidelity and hierarchical multifidelity approaches.
@article{gorodetsky2020_generalized_acv, author = {Gorodetsky, Alex A. and Geraci, Gianluca and Eldred, Michael S. and Jakeman, John D.}, title = {A generalized approximate control variate framework for multifidelity uncertainty quantification}, journal = {Journal of Computational Physics}, year = {2020}, volume = {408}, articleno = {109257}, doi = {10.1016/j.jcp.2020.109257} }We describe and analyze a variance reduction approach for Monte Carlo sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost models, which are typically lower fidelity with unknown statistics, are used to reduce the variance in statistical estimators relative to a Monte Carlo estimator with equivalent cost. We derive the conditions under which our proposed approximate control variate framework recovers existing multifidelity variance reduction schemes as special cases. We demonstrate that existing recursive or nested strategies are suboptimal because they use the additional low-fidelity models only to efficiently estimate the unknown mean of the first low-fidelity model. As a result, they cannot achieve variance reduction beyond that of a control variate estimator that uses a single low-fidelity model with known mean. However, there often exists about an order-of-magnitude gap between the maximum achievable variance reduction using all low-fidelity models and that achieved by a single low-fidelity model with known mean. We show that our proposed approach can exploit this gap to achieve greater variance reduction by using non-recursive sampling schemes. The proposed strategy reduces the total cost of accurately estimating statistics, especially in cases where only low-fidelity simulation models are accessible for additional evaluations. Several analytic examples and an example with a hyperbolic PDE describing elastic wave propagation in heterogeneous media are used to illustrate the main features of the methodology.
@article{galioto2020_bayesian_system_identification, author = {Galioto, Nicholas and Gorodetsky, Alex A.}, title = {Bayesian system ID: optimal management of parameter, model, and measurement uncertainty}, journal = {Nonlinear Dynamics}, year = {2020}, volume = {102}, number = {1}, pages = {241-267}, doi = {10.1007/s11071-020-05925-8}, url = {https://arxiv.org/abs/2003.02359} }System identification of dynamical systems is often posed as a least squares minimization problem. The aim of these optimization problems is typically to learn either propagators or the underlying vector fields from trajectories of data. In this paper, we study a first principles derivation of appropriate objective formulations for system identification based on probabilistic principles. We compare the resulting inference objective to those used by emerging data-driven methods based on dynamic mode decomposition (DMD) and system identification of nonlinear dynamics (SINDy). We show that these and related least squares formulations are specific cases of a more general objective function. We also show that the more general objective function yields more robust and reliable recovery in the presence of sparse data and noisy measurements. We attribute this success to an explicit accounting of imperfect model forms, parameter uncertainty, and measurement uncertainty. We study the computational complexity of an approximate marginal Markov chain Monte Carlo method to solve the resulting inference problem and numerically compare our results on a number of canonical systems: linear pendulum, nonlinear pendulum, the Van der Pol oscillator, the Lorenz system, and a reaction-diffusion system. The results of these comparisons show that in cases where DMD and SINDy excel, the Bayesian approach performs equally well, and in cases where DMD and SINDy fail to produce reasonable results, the Bayesian approach remains robust and can still deliver reliable results.
@article{gorodetsky2020_mfnets_bayesian_learning_prediction, author = {Gorodetsky, Alex A. and Jakeman, John D. and Geraci, Gianluca and Eldred, Michael S.}, title = {MFNETS: multifidelity data-driven networks for Bayesian learning and prediction}, journal = {International Journal of Uncertainty Quantification}, year = {2020}, volume = {10}, number = {6}, pages = {595-622}, doi = {10.1615/Int.J.UncertaintyQuantification.2020032978} }This paper presents a multifidelity uncertainty quantification framework called MFNets. We seek to address three existing challenges that arise when experimental and simulation data from different sources are used to enhance statistical estimation and prediction with quantified uncertainty. Specifically, we demonstrate that MFNets can (1) fuse heterogeneous data sources arising from simulations with different parameterizations, e.g. simulation models with different uncertain parameters or data sets collected under different environmental conditions; (2) encode known relationships among data sources to reduce data requirements; and (3) improve the robustness of existing multi-fidelity approaches to corrupted data. MFNets construct a network of latent variables (LVs) to facilitate the fusion of data from an ensemble of sources of varying credibility and cost. These LVs are posited as explanatory variables that provide the source of correlation in the observed data. Furthermore, MFNets provide a way to encode prior physical knowledge to enable efficient estimation of statistics and/or construction of surrogates via conditional independence relations on the LVs. We highlight the utility of our framework with a number of theoretical results which assess the quality of the posterior mean as a frequentist estimator and compare it to standard sampling approaches that use single fidelity, multilevel, and control variate Monte Carlo estimators. We also use the proposed framework to derive the Monte Carlo-based control variate estimator entirely from the use of Bayes rule and linear-Gaussian models -- to our knowledge the first such derivation. Finally, we use two numerical examples to demonstrate robustness and the ability to deal with heterogeneous information sources.
@article{gorodetsky2019_continuous_tensor_train, author = {Gorodetsky, Alex A. and Karaman, Sertac and Marzouk, Youssef M.}, title = {A continuous analogue of the tensor-train decomposition}, journal = {Computer Methods in Applied Mechanics and Engineering}, year = {2019}, volume = {347}, pages = {59-84}, doi = {10.1016/j.cma.2018.12.015} }We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents functions using a tensor-train ansatz by replacing the three-dimensional TT cores with univariate matrix-valued functions. The main contribution of this paper is a framework to compute the FT that employs adaptive approximations of univariate fibers, and that is not tied to any tensorized discretization. The algorithm can be coupled with any univariate linear or nonlinear approximation procedure. We demonstrate that this approach can generate multivariate function approximations that are several orders of magnitude more accurate, for the same cost, than those based on the conventional approach of compressing the coefficient tensor of a tensor-product basis. Our approach is in the spirit of other continuous computation packages such as Chebfun, and yields an algorithm which requires the computation of continuous matrix factorizations such as the LU and QR decompositions of vector-valued functions. To support these developments, we describe continuous versions of an approximate maximum-volume cross approximation algorithm and of a rounding algorithm that re-approximates an FT by one of lower ranks. We demonstrate that our technique improves accuracy and robustness, compared to TT and quantics-TT approaches with fixed parameterizations, of high-dimensional integration, differentiation, and approximation of functions with local features such as discontinuities and other nonlinearities.
@article{jakeman2019_adaptive_multi_index_collocation, author = {Jakeman, John D. and Eldred, Michael S. and Geraci, Gianluca and Gorodetsky, Alex A.}, title = {Adaptive multi-index collocation for uncertainty quantification and sensitivity analysis}, journal = {International Journal for Numerical Methods in Engineering}, year = {2019}, volume = {121}, number = {6}, pages = {1314-1343}, doi = {10.1002/nme.6268} }In this paper, we present an adaptive algorithm to construct response surface approximations of high-fidelity models using a hierarchy of lower fidelity models. Our algorithm is based on multi-index stochastic collocation and automatically balances physical discretization error and response surface error to construct an approximation of model outputs. This surrogate can be used for uncertainty quantification (UQ) and sensitivity analysis (SA) at a fraction of the cost of a purely high-fidelity approach. We demonstrate the effectiveness of our algorithm on a canonical test problem from the UQ literature and a complex multiphysics model that simulates the performance of an integrated nozzle for an unmanned aerospace vehicle. We find that, when the input-output response is sufficiently smooth, our algorithm produces approximations that can be over two orders of magnitude more accurate than single fidelity approximations for a fixed computational budget.
@article{wildey2019_robust_uq_discontinuous_functions, author = {Wildey, Timothy and Gorodetsky, Alex A. and Belme, A. and Shadid, John N.}, title = {Robust uncertainty quantification using response surface approximations of discontinuous functions}, journal = {International Journal of Uncertainty Quantification}, year = {2019}, volume = {9}, number = {5}, pages = {415-437}, doi = {10.1615/Int.J.UncertaintyQuantification.2019026974} }This paper considers response surface approximations for discontinuous quantities of interest. Our objective is not to adaptively characterize the interface defining the discontinuity. Instead, we utilize an epistemic description of the uncertainty in the location of a discontinuity to produce robust bounds on sample-based estimates of probabilistic quantities of interest. We demonstrate that two common machine learning strategies for classification, one based on nearest neighbors (Voronoi cells) and one based on support vector machines, provide reasonable descriptions of the region where the discontinuity may reside. In higher dimensional spaces, we demonstrate that support vector machines are more accurate for discontinuities defined by smooth interfaces. We also show how gradient information, often available via adjoint-based approaches, can be used to define indicators to effectively detect a discontinuity and to decompose the samples into clusters using an unsupervised learning technique. Numerical results demonstrate the epistemic bounds on probabilistic quantities of interest for simplistic models and for a compressible fluid model with a shock-induced discontinuity.
@article{alben2019_elastic_sheets, author = {Alben, Silas and Gorodetsky, Alex A. and Kim, Dong and Deegan, Robert D.}, title = {Semi-implicit methods for the dynamics of elastic sheets}, journal = {Journal of Computational Physics}, year = {2019}, volume = {399}, articleno = {108952}, doi = {10.1016/j.jcp.2019.108952} }Recent applications, e.g. active gels and self-assembly of elastic sheets, motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints that arise in explicit methods while avoiding much of the complexity of fully implicit approaches. For a triangular lattice discretization with stretching and bending springs, our semi-implicit approach involves discrete Laplacian and biharmonic operators, and is stable for all time steps in the case of overdamped dynamics. For a more general finite-difference formulation that can allow for general elastic constants, we use the analogous approach on a square grid, and find that the largest stable time step is two to three orders of magnitude greater than for an explicit scheme. For a model problem with a radial traveling wave form of the reference metric, we find transitions from quasi-periodic to chaotic dynamics as the sheet thickness is reduced, wave amplitude is increased, and damping constant is reduced.
@article{gorodetsky2018_gradient_regression_functional_tt, author = {Gorodetsky, Alex A. and Jakeman, John D.}, title = {Gradient-based optimization for regression in the functional tensor-train format}, journal = {Journal of Computational Physics}, year = {2018}, volume = {374}, pages = {1219-1238}, doi = {10.1016/j.jcp.2018.08.010} }We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient gradient computation that enables gradient-based optimization procedures, including stochastic gradient descent and quasi-Newton methods, for learning the parameters of a functional tensor-train (FT). The functional tensor-train uses the tensor-train (TT) representation of low-rank arrays as an ansatz for a class of low-multilinear-rank functions. The FT is represented by a set of matrix-valued functions that contain a set of univariate functions, and the regression task is to learn the parameters of these univariate functions. Our second contribution demonstrates that using nonlinearly parameterized univariate functions, e.g., symmetric kernels with moving centers, within each core can outperform the standard approach of using a linear expansion of basis functions. Our final contributions are new rank adaptation and group-sparsity regularization procedures to minimize overfitting. We use several benchmark problems to demonstrate at least an order of magnitude lower accuracy with gradient-based optimization methods than standard alternating least squares procedures in the low-sample number regime. We also demonstrate an order of magnitude reduction in accuracy on a test problem resulting from using nonlinear parameterizations over linear parameterizations. Finally, we compare regression performance with 22 other nonparametric and parametric regression methods on 10 real-world data sets. We achieve top-five accuracy for seven of the data sets and best accuracy for two of the data sets. These rankings are the best amongst parametric models and competitive with the best nonparametric methods.
@article{gorodetsky2018_stochastic_optimal_control_ctd, author = {Gorodetsky, Alex A. and Karaman, Sertac and Marzouk, Youssef M.}, title = {High-dimensional stochastic optimal control using continuous tensor decompositions}, journal = {International Journal of Robotics Research}, year = {2018}, volume = {37}, number = {2-3}, pages = {340-377}, doi = {10.1177/0278364917753994} }Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately, most existing algorithms that guarantee convergence to optimal solutions suffer from the curse of dimensionality: the run time of the algorithm grows exponentially with the dimension of the state space of the system. We propose novel dynamic programming algorithms that alleviate the curse of dimensionality in problems that exhibit certain low-rank structure. The proposed algorithms are based on continuous tensor decompositions recently developed by the authors. Essentially, the algorithms represent high-dimensional functions, e.g. the value function, in a compressed format, and directly perform dynamic programming computations, e.g. value iteration and policy iteration, in this format. Under certain technical assumptions, the new algorithms guarantee convergence towards optimal solutions with arbitrary precision. Furthermore, the run times of the new algorithms scale polynomially with the state dimension and polynomially with the ranks of the value function. This approach realizes substantial computational savings in compressible problem instances, where value functions admit low-rank approximations. We demonstrate the new algorithms in a wide range of problems, including a simulated six-dimensional agile quadcopter maneuvering example and a seven-dimensional aircraft perching example. In some of these examples, we estimate computational savings of up to 10 orders of magnitude over standard value iteration algorithms. We further demonstrate the algorithms running in real time on board a quadcopter during a flight experiment under motion capture.
@article{kramer2018_cur_hankel_system_identification, author = {Kramer, Boris and Gorodetsky, Alex A.}, title = {System identification via CUR-factored Hankel approximation}, journal = {SIAM Journal on Scientific Computing}, year = {2018}, volume = {40}, number = {2}, pages = {A848-A866}, doi = {10.1137/17M1137632} }Subspace-based system identification for dynamical systems is a sound, system-theoretic way to obtain linear, time-invariant system models from data. The interplay of data and systems theory is reflected in the Hankel matrix, a block-structured matrix whose factorization is used for system identification. For systems with many inputs, many outputs, or large time-series of system-response data, established methods based on the singular value decomposition (SVD), such as the eigensystem realization algorithm (ERA), are prohibitively expensive. In this paper, we propose an algorithm to reduce the complexity of the ERA from cubic to linear, with respect to the Hankel matrix size. Furthermore, our memory requirements scale at the same rate because we never require loading the entire Hankel matrix into memory. These reductions are realized by replacing the SVD with a CUR decomposition that directly seeks a low-rank approximation of the Hankel matrix. The CUR decomposition is obtained using a maximum-volume-based cross-approximation scheme that selects a small number of rows and columns to form the row and column space of the approximation. We present a worst-case error bound for our resulting system identification algorithm, and we demonstrate its computational advantages and accuracy on a numerical example. The example demonstrates that the resulting identification yields almost indistinguishable results compared with the SVD-based ERA yet comes with significant computational savings.
@article{gorodetsky2016_mercer_kernels_integrated_variance, author = {Gorodetsky, Alex A. and Marzouk, Youssef M.}, title = {Mercer kernels and integrated variance experimental design: connections between Gaussian process regression and polynomial approximation}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, year = {2016}, volume = {4}, number = {1}, pages = {796-828}, doi = {10.1137/15M1017119} }This paper examines experimental design procedures used to develop surrogates of computational models, exploring the interplay between experimental designs and approximation algorithms. We focus on two widely used approximation approaches, Gaussian process (GP) regression and non-intrusive polynomial approximation. First, we introduce algorithms for minimizing a posterior integrated variance (IVAR) design criterion for GP regression. Our formulation treats design as a continuous optimization problem that can be solved with gradient-based methods on complex input domains, without resorting to greedy approximations. We show that minimizing IVAR in this way yields point sets with good interpolation properties, and that it enables more accurate GP regression than designs based on entropy minimization or mutual information maximization. Second, using a Mercer kernel/eigenfunction perspective on GP regression, we identify conditions under which GP regression coincides with pseudospectral polynomial approximation. Departures from these conditions can be understood as changes either to the kernel or to the experimental design itself. We then show how IVAR-optimal designs, while sacrificing discrete orthogonality of the kernel eigenfunctions, can yield lower approximation error than orthogonalizing point sets. Finally, we compare the performance of adaptive Gaussian process regression and adaptive pseudospectral approximation for several classes of target functions, identifying features that are favorable to the GP + IVAR approach.
@article{gorodetsky2014_localization_discontinuities, author = {Gorodetsky, Alex A. and Marzouk, Youssef M.}, title = {Efficient localization of discontinuities in complex computational simulations}, journal = {SIAM Journal on Scientific Computing}, year = {2014}, volume = {36}, number = {6}, pages = {A2584-A2610}, doi = {10.1137/140953137} }Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, the error and convergence rate of many approximation methods deteriorate substantially. This paper details a method for efficiently localizing discontinuities in the input parameter domain, so that the model output can be approximated as a piecewise smooth function. The approach comprises an initialization phase, which uses polynomial annihilation to assign function values to different regions and thus seed an automated labeling procedure, followed by a refinement phase that adaptively updates a kernel support vector machine representation of the separating surface via active learning. The overall approach avoids structured grids and exploits any available simplicity in the geometry of the separating surface, thus reducing the number of model evaluations required to localize the discontinuity. The method is illustrated on examples of up to eleven dimensions, including algebraic models and ODE/PDE systems, and demonstrates improved scaling and efficiency over other discontinuity localization approaches.
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Conference papers
@inproceedings{dixon2026_distribution_estimation_aerospace, author = {Dixon, Thomas O. and Bomarito, Geoffrey F. and Geraci, Gianluca and Warner, James E. and Pribe, Joshua and Eldred, Michael S. and Gorodetsky, Alex A.}, title = {A multi-fidelity approach to distribution estimation applied to aerospace applications}, booktitle = {AIAA SCITECH 2026 Forum}, year = {2026}, doi = {10.2514/6.2026-2024} }Multi-fidelity methods for Monte Carlo sampling are efficient strategies to perform forward uncertainty quantification in high-dimensional, nonlinear settings where surrogate construction is difficult. These methods are based on the classical Monte Carlo estimator, but fuse predictions from two or more models of varying fidelity to obtain estimators with greater precision, given a prescribed computational budget. Despite their success, most of these multi-fidelity methods are designed to estimate statistical moments, for example mean and variance, while the majority of existing multi-fidelity distribution estimation methods require known model hierarchies. In this work, we extend the approximate control variate approach to estimate cumulative distribution functions using multi-output estimation. A regression technique is also introduced to improve estimator accuracy by smoothing out statistical noise. We present results on the evaluation of distributions for applications like entry, descent, and landing and additively manufactured Ni-base superalloys.
@inproceedings{whittaker2026_spt140_bayesian_calibration, author = {Whittaker, Collin B. and Marks, Thomas A. and Gorodetsky, Alex A.}, title = {Bayesian calibration of a multi-component model of the SPT-140 Hall thruster}, booktitle = {AIAA SCITECH 2026 Forum}, year = {2026}, doi = {10.2514/6.2026-0066} }We deploy the Joint Advanced Propulsion Institute's Hall thruster Predictive Engineering Model on the SPT-140 system qualified and flown for NASA's Psyche spacecraft. The purpose of the Predictive Engineering Model is to enable rapid predictions and uncertainty quantification of system performance while accounting for facility effects associated with ground-based testing. The most recent instantiation of the Predictive Engineering Model framework consists of an analytical model predicting cathode coupling voltage, a one-dimensional axial fluid Hall thruster code predicting the main discharge, and an analytical plume expansion model predicting ion current density traces. The primary facility effect they capture is background pressure. To deploy the Predictive Engineering Model for the SPT-140, we extended the models to enable scaling the Hall thruster's magnetic field at different operating conditions. We then calibrated the Predictive Engineering Model using data from ground qualification tests performed by NASA's Jet Propulsion Laboratory. These datasets include thrust, discharge current, and ion acceleration measurements. A Bayesian calibration of the model parameters yields a posterior consistent with previous calibrations on the SPT-100 and H9 thrusters. Unlike standard practice, where anomalous collisions are calibrated to individual operating conditions, we use a single anomalous transport model parameterized by pressure. Thus we provide initial evidence for predictive capabilities of target quantities of interest. Following calibration, we extrapolate the model predictions to vacuum. Thrust predictions at higher powers are shown to be comparable to modeling by the Jet Propulsion Laboratory using Hall2De done during qualification, while discharge current data are not reliably predicted. The mismatch of discharge current is attributed to the fact that the Predictive Engineering Model assumes a fixed anomalous collision frequency profile whose position shifts with pressure.
@inproceedings{wentz2026_transfer_learning_hall_thrusters, author = {Wentz, Jacqueline and Marks, Thomas A. and Geraci, Gianluca and Davis, Owen and Eldred, Michael S. and Gorodetsky, Alex A.}, title = {Improving the efficiency of multi-fidelity approaches for transfer learning with application to Hall thrusters}, booktitle = {AIAA SCITECH 2026 Forum}, year = {2026}, doi = {10.2514/6.2026-2025} }In this paper, we extend Multi-fidelity Networks for transfer learning in the context of engineering system performance prediction. Multi-fidelity Networks build a surrogate representation of multiple information sources and encode the relationship among these sources as a directed acyclic graph. Each information source corresponds to a node on the graph, and relationships between the sources are represented as edges. In this paper we introduce a greedy procedure that adaptively learns the best polynomial degree for each node. Moreover, the algorithm uses the polynomial degree adaptation to drive the allocation of resources needed at each node, namely the number of model realizations. Our goal is to deploy this strategy to leverage existing data from systems at well-explored missions and operative conditions, when data are abundant or can be obtained easily, to predict the performance of a novel system in a different operative scenario where less data is available. As an exemplar application, we target the prediction of in-flight Hall thruster performance using both ground-test data and data from other Hall thruster systems. Specifically, we consider a hypothetical interplanetary mission, where we seek to estimate the performance, thrust, of the H9 Hall thruster given uncertain electron transport and neutral gas velocity. A limited dataset of simulated H9 thrust values is augmented with a larger dataset from the Stationary Plasma Thruster system. To construct the Stationary Plasma Thruster dataset, we perform simulations that are representative of both ground testing and interplanetary flight and include multiple fidelity levels for each of these configurations. This allows us to test various scenarios to determine if the adaptive algorithm can successfully leverage information from lower-cost systems to predict the performance of the H9 Hall thruster.
@inproceedings{eckels2025_sliding_window_hall_thruster, author = {Eckels, Joshua D. and Lopez Ortega, Alejandro and Gorodetsky, Alex A.}, title = {Data-driven acceleration of Hall thruster simulations with a sliding-window method}, booktitle = {International Electric Propulsion Conference}, year = {2025}, url = {https://www.electricrocket.org/IEPC_2025/London/submission_41.pdf}, note = {IEPC-2025-041} }This work develops an online method for robustly training data-driven reduced-order models for Hall thruster plasma simulations. Startup transients from simulation initialization are known to degrade long-term prediction accuracy of reduced-order models, so it is desirable for both training reduced-order models and terminating simulations to accurately detect the end of transience. To this end, the dynamic mode decomposition is applied within a sliding-window algorithm to detect end of transience in the Hall2De fluid simulation code. The sliding-window method is shown to accurately detect the relaxation of simulation startup transients using a non-intrusive, data-driven approach. Furthermore, the method produces a reduced-order model with more accurate long-term predictions compared to a reduced-order model trained naively on initial simulation data, in some cases by an order of magnitude. Acceleration of the Hall2De simulation is achieved by early termination of the expensive physics solver. Nonlinear effects are observed to limit the accuracy of the method, which may be addressed in future work by using extensions to dynamic mode decomposition or nonlinear alternatives.
@inproceedings{wang2025_factorization_online_variational_inference, author = {Wang, Liliang and Gorodetsky, Alex A.}, title = {Factorization-based online variational inference for state-parameter estimation of partially observable nonlinear dynamical systems}, booktitle = {AIAA SCITECH 2025 Forum}, year = {2025}, doi = {10.2514/6.2025-1960} }We propose an online variational inference framework for joint parameter-state estimation in nonlinear systems. This approach provides a probabilistic estimate of both parameters and states, and does so without relying on a mean-field assumption of independence of the two. The proposed method leverages a factorized form of the target posterior distribution to enable an effective pairing of variational inference for the marginal posterior of parameters with conditional Gaussian filtering for the conditional posterior of the states. This factorization is retrained at every time step via a formulation that combines variational inference and regression. The effectiveness of the framework is demonstrated through applications to two example systems, where it outperforms both the joint Unscented Kalman Filter and Bootstrap Particle Filter parameter-state augmentation in numerical experiments.
@inproceedings{wentz2025_multifidelity_bayesian_networks_transfer_learning, author = {Wentz, Jacqueline and Geraci, Gianluca and Davis, Owen and Eldred, Michael S. and Jakeman, John D. and Mustaev, Artem and Gorodetsky, Alex A.}, title = {Multi-fidelity Bayesian networks for transfer learning in modular systems}, booktitle = {AIAA SCITECH 2025 Forum}, year = {2025}, doi = {10.2514/6.2025-1961} }The design of new systems and the accreditation of systems in new operating environments are demanding tasks, requiring extensive simulations and experiments of the new design and/or the new environment. This cost can sometimes be mitigated by leveraging previously accumulated knowledge from related systems or missions, in the case where the key differences can be adequately characterized. In this work, we investigate the efficacy of transfer learning based on a novel application of Multi-fidelity Bayesian Networks. In addition to the current usage of Multi-fidelity Bayesian Networks for managing different levels of model fidelity using a network of surrogate models, here we expand the scope to include incorporating data from multiple system definitions, multiple subsystem configurations, and multiple operational missions. We demonstrate the effectiveness of our approach on a structural dynamics system with multiple combinations of system, configuration, mission, and fidelity and with differing levels of available data for these combinations, and we study different network topologies to gain intuition as to their capabilities for this task. Our numerical results show that Bayesian network surrogate modeling has the potential to characterize the performance of new systems and missions, strengthening the linkage between multifidelity modeling and transfer learning.
@inproceedings{marks2025_kinetic_axial_azimuthal_hall_thruster, author = {Marks, Thomas A. and Gorodetsky, Alex A.}, title = {Towards kinetic axial-azimuthal Hall thruster simulations including ionization}, booktitle = {International Electric Propulsion Conference}, year = {2025}, url = {https://www.electricrocket.org/IEPC_2025/London/submission_129.pdf}, note = {IEPC-2025-0129} }The open-source particle-in-cell code WarpX is used to perform two-dimensional axial-azimuthal Hall thruster simulations including a neutral population and self-consistent ionization using the direct simulation Monte Carlo method. The results of these simulations are assessed in comparison to similar simulations which use a static particle source. The time-averaged simulation outputs for the direct simulation Monte Carlo simulations differ from those without; in particular, the electron temperature and anomalous drag force are higher and the electric field is less strongly peaked. The time-dependent outputs show strong ion density oscillations, consistent with the well-known Hall thruster breathing mode. The relative phasing of this oscillation with respect to other plasma properties is examined, with inconclusive results. Ion recombination at the anode is assessed and found to increase the amplitude of breathing mode oscillations. Numerical challenges encountered in these simulations are discussed, particularly the large fluctuations in particle count during thruster startup and over the course of the oscillations. The findings highlight the advantages of GPU computing and semi-implicit schemes in enabling kinetic Hall thruster simulations to reach new physical regimes, as well as avenues for future improvement.
@inproceedings{dixon2024_bifidelity_optimization_under_uncertainty, author = {Dixon, Thomas O. and Gorodetsky, Alex A.}, title = {A bi-fidelity strategy for optimization under uncertainty with applications to aircraft trajectory optimization}, booktitle = {AIAA SCITECH 2024 Forum}, year = {2024}, doi = {10.2514/6.2024-1025} }We test a simple bi-fidelity strategy for accelerating trajectory optimization under uncertainty in the presence of robust constraints. Our approach combines the accuracy of high-fidelity models with the computational efficiency of low-fidelity counterparts to increase the accuracy of constraint computation for a given cost. Specifically, we accelerate sample-average approaches that use high-fidelity models with additional samples of low-fidelity models for assessing whether or not a risk constraint is violated. The low-fidelity model's purpose is thus to reduce the uncertainty in the estimate of constraint violation, at the expense of the introduction of bias. Our empirical test on a simulation of glider dynamics tasked with avoiding a region indicates an order-of-magnitude fewer failures using the bi-fidelity strategy.
@inproceedings{aksoy2024_compressed_ep_tensors, author = {Aksoy, Doruk and Vutukury, Sruti and Marks, Thomas A. and Eckels, Joshua D. and Gorodetsky, Alex A.}, title = {Compressed analysis of electric propulsion simulations using low rank tensor networks}, booktitle = {International Electric Propulsion Conference}, year = {2024}, url = {https://electricrocket.org/IEPC_2024/795.pdf}, note = {IEPC-2024-795} }This work presents an approach to mitigate high storage and computational costs associated with analysis of high-fidelity simulation data. Specifically, we demonstrate that low-rank tensor compression of field quantities from particle-based plasma simulation data of electric propulsion devices can yield significant benefits. Moreover, compression in low-rank tensor format enables doing typical analysis without decompression. Our test case is a 3D simulation of an SPT-100 thruster operating in vacuum using AFRL's Thermophysics Universal Research Framework (TURF) code. We measure the TT-ICE method's performance on the simulation data based on compression ratio, compression time, and integrity of the reconstructed dataset to the original. For particle number densities stored in structured meshes, we achieve a compression ratio (CR) of 8.08x. For ion current density and electric field components, we achieve a CR of 6.23x and 354,796x, respectively. For unstructured surface mesh data, we see near exact floating potential approximations and derived total current to surface quantities.
@inproceedings{eckels2024_dmd_hall_thruster_plume, author = {Eckels, Joshua D. and Marks, Thomas A. and Aksoy, Doruk and Vutukury, Sruti and Gorodetsky, Alex A.}, title = {Dynamic mode decomposition for particle-in-cell simulations of a Hall thruster and plume}, booktitle = {International Electric Propulsion Conference}, year = {2024}, url = {https://electricrocket.org/IEPC_2024/412.pdf}, note = {IEPC-2024-412} }In this work, we target the acceleration of particle-in-cell (PIC) methods for Hall thrusters by way of data-driven reduced-order modeling through the dynamic mode decomposition (DMD). The primary goal of data-driven reduced-order modeling is to learn a system's dynamics from observations of its state over time. Once obtained, the reduced-order model can be used in place of the original system for cheap forecasting of its state. In this work, we build reduced-order models for the dynamics of kinetic PIC simulations of a Hall thruster plasma. Specifically, we apply the linear DMD approximation to a fully kinetic simulation of a Hall thruster discharge channel and separately to a 3D hybrid fluid/PIC simulation of a Hall thruster plume. We found that a rank-truncated linear fit is sufficient to qualitatively, and sometimes quantitatively, predict the primary modes of the plasma dynamics, including the azimuthal wave propagations in the discharge channel that are indicative of the electron drift instability. We also observed that high-noise, high-dimensional, and multi-scale behavior presents a computational challenge for efficiently and accurately fitting PIC simulations. With further refinement, we envision that kinetic reduced-order models of a Hall thruster have potential use in downstream applications such as online control and closure modeling.
@inproceedings{marks2024_warpx_iepc, author = {Marks, Thomas A. and Gorodetsky, Alex A.}, title = {Hall thruster simulations in WarpX}, booktitle = {International Electric Propulsion Conference}, year = {2024}, url = {https://electricrocket.org/IEPC_2024/409.pdf}, note = {IEPC-2024-409} }Two-dimensional axial-azimuthal simulations of a Hall thruster are performed using the open-source particle-in-cell code WarpX. The simulation conditions are chosen to match those of the LANDMARK axial-azimuthal benchmark reported by Charoy et al. in 2019. Additionally, a range of numerical and solver parameters are investigated in order to find those which yield the best performance. By extending the code via its Python interface, it is found that WarpX can simulate the benchmark case in 3.8 days on an Nvidia V100 hailing from the same era as the original benchmark, and in just 1.8 days on a more recent Nvidia H100 GPU. Of the numerical parameters investigated, it is determined that the field-solve tolerance and particle resampling thresholds have the largest effect on the simulation wall time, but that particle resampling may artificially widen electron velocity distribution functions, leading to unphysical heating. Using the results of the parameter investigation, an optimized simulation is then performed which completes the benchmark in just 36 hours on a single GPU. The results of this work are discussed in the context of advancements in GPU hardware and the suitability of kinetic Hall thruster simulations for engineering applications.
@inproceedings{allen2024_oed_hall_thruster_transport, author = {Allen, Madison G. and Marks, Thomas A. and Eckels, Joshua D. and Gorodetsky, Alex A. and Jorns, Benjamin A.}, title = {Optimal experimental design for inferring anomalous electron transport in a Hall thruster}, booktitle = {AIAA SCITECH 2024 Forum}, year = {2024}, doi = {10.2514/6.2024-2164} }Optimal experimental design is applied to reduce the number of laser-induced fluorescence measurements required to calibrate the parameters of an anomalous electron transport model in a multi-fluid, one-dimensional Hall thruster model. The time-averaged velocity data from the channel centerline of the SPT-100 Hall effect thruster is used as the dataset for calibrating a multi-zone Bohm model for electron transport. This dataset is then sub-sampled with an optimal experimental design algorithm employing a batch method based on the expected information gain metric. It is shown that a batch with only 25% of the data points can yield model calibrations that match the median calibration from a full dataset, though the variance in the batch result is higher. This finding is discussed in the context of designing experimental efforts where time and resources are limited.
@inproceedings{lipscomb2024_vacuum_chamber_surrogate_uq, author = {Lipscomb, Charles P. and Boyd, Iain D. and Hansson, Kaelan B. and Eckels, Joshua D. and Gorodetsky, Alex A.}, title = {Simulation of vacuum chamber pressure distribution with surrogate modeling and uncertainty quantification}, booktitle = {AIAA SCITECH 2024 Forum}, year = {2024}, doi = {10.2514/6.2024-2369} }A major challenge in understanding differences in electric propulsion performance in ground tests and in space operations concerns the pressure distribution within the test vacuum chamber. The chamber backpressure is much higher than experienced in space, modifying thruster performance and plume dynamics. Numerical simulation is a key element in determining the background conditions in non-ideal vacuum chamber environments. An important parameter for the accurate simulation of chamber backpressure is the probability that an atom will stick to a cryogenic panel used to pump away the plume gases. This quantity can be used to model vacuum pumps in particle-based kinetic numerical methods. In this work, a three-dimensional direct simulation Monte Carlo code is used to model neutral xenon atoms flowing from the anode of the H9 Hall Effect Thruster within the University of Michigan's Large Vacuum Test Facility. Simulated pressures are compared with ion gauge pressure measurements to infer the effective sticking coefficient of the chamber's vacuum pumps. A pressure-predicting surrogate model is developed for inference of pump sticking coefficients and for uncertainty quantification. This information enables accurate and useful kinetic simulations of electric propulsion thruster plasma plumes in vacuum chambers.
@inproceedings{zeng2023_basis_adaptation_scitech, author = {Zeng, Xiaoshu and Geraci, Gianluca and Gorodetsky, Alex A. and Jakeman, John D. and Eldred, Michael S. and Ghanem, Roger G.}, title = {Improving Bayesian networks multifidelity surrogate construction with basis adaptation}, booktitle = {AIAA SCITECH 2023 Forum}, year = {2023}, doi = {10.2514/6.2023-0917} }Surrogate construction is an essential component for all non-deterministic analyses in science and engineering. The efficient construction of easy and cheaper-to-run alternatives to a computationally expensive code paves the way for outer-loop workflows for forward and inverse uncertainty quantification and optimization. Unfortunately, the accurate construction of a surrogate still remains a task that often requires a prohibitive number of computations, making the approach unattainable for large-scale and high-fidelity applications. Multifidelity approaches offer the possibility to lower the computational expense requirement on the high-fidelity code by fusing data from additional sources. In this context, we have demonstrated that multifidelity Bayesian Networks can efficiently fuse information derived from models with an underlying complex dependency structure. In this contribution, we expand on our previous work by adopting a basis adaptation procedure for the selection of the linear model representing each data source. Our numerical results demonstrate that this procedure is computationally advantageous because it can maximize the use of limited data to learn and exploit the important structures shared among models. Two examples are considered to demonstrate the benefits of the proposed approach: an analytical problem and a nuclear fuel finite element assembly. From these two applications, a lower dependency of MFNets on the model graph has also been observed.
@inproceedings{mckenna2023_dynamic_soaring_parameter_estimation, author = {McKenna, Carleen and Gorodetsky, Alex A.}, title = {Online parameter estimation within trajectory optimization for dynamic soaring}, booktitle = {AIAA SCITECH 2023 Forum}, year = {2023}, doi = {10.2514/6.2023-1482} }We propose a novel control architecture incorporating online parameter estimation alongside model predictive control with application to dynamic soaring. Dynamic soaring is a process that has prompted recent research which allows a UAV to extract energy from wind gradients to stay aloft, thereby minimizing the need for propulsive action during flight. However, to properly execute dynamic soaring maneuvers sufficient information about the wind gradient and aerodynamic properties of the UAV is required. Much of the research on dynamic soaring has focused on offline trajectory optimization. Either no estimation of parameters is incorporated, or estimation serves to inform decisions based on an existing library of trajectories or neural networks trained on offline-generated data points. Other work has been done on online trajectory planning in the form of model predictive control, but estimation is rarely incorporated. Our proposed algorithm combines parameter estimation with online trajectory optimization to create a risk-aware framework which is able to select control inputs to minimize the impact of uncertainty and learn the true values of environmental and aerodynamic parameters. We also show that our sequential Monte Carlo based online parameter estimation method performs similarly under identical conditions to Markov chain Monte Carlo. We also establish deterministic model predictive control as a baseline and show that our algorithm performs similarly to deterministic model predictive control with known parameters. In a comparison of deterministic model predictive control with known parameters, deterministic model predictive control with unknown parameters, and our algorithm, we show the positive impact of learning on the ability of model predictive control to maintain energy levels throughout the soaring process. Finally, after a robustness analysis, we report good performance of the algorithm under a variety of conditions both generally and in comparison to deterministic model predictive control.
@inproceedings{eckels2023_oed_porous_electrosprays, author = {Eckels, Joshua D. and Whittaker, Collin B. and Jorns, Benjamin A. and Gorodetsky, Alex A.}, title = {Optimal experimental design to learn reduced-fidelity models for porous electrosprays}, booktitle = {AIAA SCITECH 2023 Forum}, year = {2023}, doi = {10.2514/6.2023-0066} }The task of scaling electrospray thrusters to missions with higher thrust requirements is one of seeking robust designs in the presence of high manufacturing uncertainties. The ability to explore the large design space of electrosprays is largely prohibited by the time and cost of prototyping, and by the computational expense of numerical models that are able to fully capture detailed physics. Reduced-fidelity models offer the ability to more efficiently search the design space of electrosprays by using analytical scaling laws and phenomenological relationships to represent complex physics and to reduce computational expense. By nature, these reduced-fidelity models require the collection of experimental data to calibrate phenomenological parameters before they can be applied to the task of design optimization. An additional challenge for calibrating reduced-fidelity models for electrosprays is the presence of high uncertainty in other nuisance parameters that clouds knowledge of the desired calibration model parameters. In this study, we use the Bayesian framework of optimal experimental design to identify the experimental operating conditions that are most informative for calibrating reduced-fidelity model parameters for porous electrospray thrusters in the presence of high manufacturing uncertainties. We first introduce the optimal experimental design formulation of expected information gain for an experiment with a marginalization framework for managing uncertainty in nuisance parameters. Then, we compare the performance of two estimators of the expected information gain on a linear model, a nonlinear model, and a current emission model for a porous emitter array. We find that a simple linear approximation of the forward model can be used to obtain significant computational speedup in estimating the expected information gain for experimental design. In addition, we show the limitations of applying previous estimators to models of varying form, namely that the scaling of sample allocations is highly dependent on the model form.
@inproceedings{thompson2023_automation_model_tuning, author = {Thompson, Marten and Geraci, Gianluca and Bomarito, Geoffrey F. and Warner, James E. and Leser, Patrick and Leser, William P. and Eldred, Michael S. and Jakeman, John D. and Gorodetsky, Alex A.}, title = {Strategies for automation of model tuning in multi-fidelity trajectory uncertainty propagation}, booktitle = {AIAA SCITECH 2023 Forum}, year = {2023}, doi = {10.2514/6.2023-1481} }Multi-model Monte Carlo methods are efficient strategies to perform forward uncertainty quantification studies in entry, descent, and landing (EDL) applications. These multi-model methods are based on the classical Monte Carlo estimator, but fuse predictions from several low-fidelity models to obtain estimators with greater precision given a prescribed computational budget. The effectiveness of these approaches relies on the magnitudes of correlations between the low-fidelity models and the high-fidelity model, as well as the relative computational costs of all models. Identifying and exploiting the best trade-off between correlation and cost, which ultimately depends on the selection of hyperparameters in the low-fidelity models, is a task often performed by hand or simply inspired by the deterministic understanding available for a specific application. This work extends a preliminary effort, which demonstrated the importance of automatic and optimal tuning of hyperparameters to obtain efficient multi-model estimators. New optimization strategies are compared to gauge their feasibility and limitations for realistic applications, e.g., by accounting for their computational demand. The Sandia National Laboratories software Dakota, which supports a variety of multi-model estimators and optimization algorithms, is employed in all numerical examples for both analytical tests and EDL calculations. A case study in the Adaptable, Deployable Entry and Placement Technology (ADEPT) project trajectory simulations demonstrates the practical advantages of the proposed framework.
@inproceedings{whittaker2022_multisite_emission_electrosprays, author = {Whittaker, Collin B. and Eckels, Joshua D. and Gorodetsky, Alex A. and Jorns, Benjamin A.}, title = {A moment-based model of multi-site emission for porous electrosprays}, booktitle = {International Electric Propulsion Conference}, year = {2022}, url = {https://www.jotform.com/uploads/electricrocket/220994246997171/5321569065654908601/IEPC_2022_Whittaker_C_1.pdf} }A reduced fidelity model for the formation of and emission from multiple Taylor cone structures on a porous electrospray emitter is formulated. The model is predicated on balancing internal pressure against electrostatic pressure for a given location on the cone. The probability of multi-site emission is assessed by considering the porosity, cone dimensions, and distribution of applied electric field. There are five free parameters of the model, which are determined by applying the method of hierarchical Bayesian inference to an existing set of experimental measurements of number of emission sites and emitter current as a function of applied voltage. Subject to this inference, the model is found to reproduce the experimentally observed behavior. It is found, however, that the inferred distribution of menisci properties disagrees with the properties of the substrate pores. This discrepancy is discussed within the context of possible propellant pooling.
@inproceedings{sharma2022_nonseparable_hamiltonian_cdc, author = {Sharma, Harsh and Galioto, Nicholas and Gorodetsky, Alex A. and Kramer, Boris}, title = {Bayesian identification of nonseparable Hamiltonian systems using stochastic dynamic models}, booktitle = {IEEE Conference on Decision and Control}, year = {2022}, pages = {6742-6749}, doi = {10.1109/CDC51059.2022.9992571}, url = {https://arxiv.org/abs/2209.07646} }This paper proposes a probabilistic Bayesian formulation for system identification and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse science and engineering applications such as astrophysics, robotics, vortex dynamics, charged particle dynamics, and quantum mechanics. The numerical experiments demonstrate that the proposed method recovers dynamical systems with higher accuracy and reduced predictive uncertainty compared to state-of-the-art approaches. The results further show that accurate predictions far outside the training time interval in the presence of sparse and noisy measurements are possible, which lends robustness and generalizability to the proposed approach. A quantitative benefit is prediction accuracy with less than 10% relative error for more than 12 times longer than a comparable least-squares-based method on a benchmark problem.
@inproceedings{bomarito2022_model_selection_tuning, author = {Bomarito, Geoffrey F. and Geraci, Gianluca and Warner, James E. and Leser, Patrick and Leser, William P. and Eldred, Michael S. and Jakeman, John D. and Gorodetsky, Alex A.}, title = {Improving multi-model trajectory simulation estimators using model selection and tuning}, booktitle = {AIAA SCITECH 2022 Forum}, year = {2022}, doi = {10.2514/6.2022-1099} }Multi-model Monte Carlo methods have been demonstrated to be an efficient and accurate alternative to standard Monte Carlo in the model-based propagation of uncertainty in entry, descent, and landing applications. These multi-model Monte Carlo methods fuse predictions from low-fidelity models with the high-fidelity entry, descent, and landing model of interest to produce unbiased statistics with a fraction of the computational cost. The accuracy and efficiency of the multi-model Monte Carlo methods are dependent upon the magnitude of correlations of the low-fidelity models with the high-fidelity model, but also upon the correlation among the low-fidelity models, and their relative computational cost. Because of this layer of complexity, the question of how to optimally select the set of low-fidelity models has remained open. In this work, methods for optimal model construction and tuning are investigated as a means to increase the speed and precision of trajectory simulation for entry, descent, and landing. Specifically, the focus is on the inclusion of low-fidelity model tuning within the sample allocation optimization that accompanies multi-model Monte Carlo methods. Preliminary results indicate that low-fidelity model tuning can significantly improve efficiency and precision of trajectory simulations and provide an increased edge to multi-model Monte Carlo methods when compared to standard Monte Carlo. The challenges and potential benefits to exploring a fully iterative and comprehensive optimization strategy in future work are highlighted.
@inproceedings{whittaker2022_model_inference_electrospray_array, author = {Whittaker, Collin B. and Gorodetsky, Alex A. and Jorns, Benjamin A.}, title = {Model inference from electrospray thruster array tests}, booktitle = {AIAA SCITECH 2022 Forum}, year = {2022}, doi = {10.2514/6.2022-0041} }A model for the current emitted by a porous conical-type electrospray array is formulated by considering the operation of individual emitters in parallel. The individual emitter behavior is determined from five interrelated models: one predicting the current sourced by an individual emission site based on the feeding conditions of the substrate and the applied electric field, another predicting the number and size of such sites for a given emitter, a model which calculates the electric field at the emitter from the applied voltage, and lastly models which predict the characteristic fluid flow impedance and the electric field as a function of device geometry. A Bayesian inference problem over the associated model parameters is constructed, incorporating an approximate pseudomarginalization over the device geometry and other nuisance parameters of the model to propagate their uncertainty. This inference is performed considering experimental data and thruster geometry for a 576 emitter array developed by the Air Force Research Laboratory. Samples from the resulting posterior distribution over parameters are drawn and subsequently used to make predictions for the device behavior, which is contrasted with that observed experimentally. It is determined that if the variability in emitter geometry is neglected, the model is unable to reproduce the experimental behavior; by accounting for this effect, however, the model matches experimental observations. This contrast in model agreement is discussed in the context of the role of manufacturing tolerance on emitter performance and in the design of similar systems in the literature. Limitations on the extensibility of the ionic emission model are also examined in light of the fact that there is a possible correlation between the model parameters and geometry.
@inproceedings{walker2022_janus_overview, author = {Walker, Mitchell L. R. and Lev, Dan and Saeedifard, Maryam and Jorns, Benjamin A. and Foster, John and Gallimore, Alec D. and Gorodetsky, Alex A. and Rovey, Joshua L. and Chew, Huck Beng and Levin, Deborah and Williams, John D. and Yalin, Azer and Wirz, Richard E. and Marian, Jaime and Boyd, Iain D. and Hara, Kentaro and Lemmer, Kristina}, title = {Overview of the Joint Advanced Propulsion Institute (JANUS)}, booktitle = {International Electric Propulsion Conference}, year = {2022}, url = {https://www.jotform.com/uploads/electricrocket/220994246997171/5316003891316539828/IEPC-2022-156.pdf} }The Joint AdvaNced PropUlsion InStitute (JANUS) is a NASA-funded endeavor to enable and proliferate the flight of high-power electric propulsion systems. Successful completion of this five-year effort will establish physics-based limits, mitigation techniques, and extrapolation procedures to provide a probabilistic assessment of the in-space performance and lifetime of high-power, approximately 100 kW, electric propulsion devices. The assessment will come from measurements made in ground-based test facilities combined with predictive engineering models. To realize this vision requires a significant advance in the understanding of the limitations of test facilities, physics-based numerical models, mitigation technique efficacy, and in-space operation of electric propulsion devices. To do so, JANUS addresses four interdependent research pillars: Thruster Testing, Facility Fidelity, Diagnostics and Fundamental Studies, and Physics-based Modeling and Integration. JANUS uses uncertainty quantification and sensitivity analysis for each pillar of all performance and life models. Specifically, the work focuses on Hall-effect thrusters and gridded ion thrusters operating on xenon and krypton gases. This effort will deliver several new tools, strategies, and guidelines for evaluating existing infrastructure and designing new infrastructure for testing high-power electric propulsion. To achieve this, JANUS has mobilized a team of researchers who are subject-matter experts in the relevant research areas. The home institutions of the principal participants are Georgia Institute of Technology, University of Michigan, University of California Los Angeles, University of Illinois, Colorado State University, University of Colorado, Stanford University, and Western Michigan University. JANUS collaborates with government and industry partners to incorporate the advancements into present and future research and development processes.
@inproceedings{wirz2022_predictive_engineering_model_ep, author = {Wirz, Richard E. and Gorodetsky, Alex A. and Jorns, Benjamin A. and Walker, Mitchell L. R.}, title = {Predictive engineering model for life and performance assessment of high-power electric propulsion systems}, booktitle = {International Electric Propulsion Conference}, year = {2022}, url = {https://www.jotform.com/uploads/electricrocket/220994246997171/5952278425021935072/Wirz_IEPC-2022-410_PEM.pdf} }The Joint AdvaNced PropUlsion InStitute (JANUS) is using a Predictive Engineering Model (PEM) framework to assess the life and performance of NASA's high-power electric propulsion systems. The primary challenge for accurate assessment is accounting for the relatively extreme facility effects encountered during ground-based testing of high-power, high-flowrate electric propulsion devices. The Predictive Engineering Modeling framework utilizes a combination of multifidelity, multiphysics models of physical processes with models of the propulsion system, environment, and power electronics to assess thruster performance and life. These models work together with a governing PEM framework to provide integrated, holistic simulations of the system behavior in different vacuum facilities. Differences between the facility and in-space behavior, and optimization efforts to reduce these differences, are used to inform facility effect mitigation strategies. Uncertainty quantification will provide probabilistic extrapolations to in-space performance and life, and feedback to guide experimental and high-fidelity simulation campaigns needed to improve model accuracy. As such, the PEM provides a multidisciplinary and multi-participant framework for making significant progress towards confidently predicting the life and performance of high-power electric propulsion systems.
@inproceedings{eckels2022_electrospray_geometry_surrogate, author = {Eckels, Joshua D. and Whittaker, Collin B. and Gorodetsky, Alex A. and Jorns, Benjamin A. and St. Peter, Benjamin and Dressler, Rainer A.}, title = {Simulation-based surrogate methodology of electric field for electrospray emitter geometry design and uncertainty quantification}, booktitle = {International Electric Propulsion Conference}, year = {2022}, url = {https://www.jotform.com/uploads/electricrocket/220994246997171/5314815798819330058/IEPC_2022%25285%2529.pdf} }Electrospray thruster technology requires the use of arrayed emitter and extractor grid structures to scale thrust to mission operation levels. With recent advances in manufacturing capabilities of porous-media emitter substrates, a design space opens where more control is given over the geometry of individual emitters in an arrayed structure. For many electrospray design applications, a quantity of interest for evaluating performance and efficiency of emitters is the peak electric field strength near the tip of the emitter. The mapping between the geometry design space of emitters and the resulting electric field for a given bias voltage is not analytically available; this study proposes a simulation and surrogate methodology for the prediction of peak electric field strength based on the geometry parameters of an individual emitter. An electrostatic partial differential equation solver was used to generate an electric field solution at all design considerations. The maximum electric field magnitude was then extracted and used as training data for a surrogate model to be used in an engineering toolkit for mapping geometry parameters to maximum electric field. The surrogate was found to significantly outperform existing models in the toolkit on average over the design space considered, with a median error of 6% vs. 160% for the existing models. Finally, the computational advantage of the surrogate enabled a global sensitivity analysis of the peak electric field. Variance in output electric field predictions was found to be most attributable to uncertainties in the radius of curvature at the tip of the emitter and the slant angle of the emitter cone.
@inproceedings{yang2022_wet_clutch_restart_uq, author = {Yang, Hang and Fujii, Yuji and Zhang, Yijing and Haria, Hiral and Devendran, Ram Sudarsan and Saini, Ankit and Gorodetsky, Alex A. and Wang, Kon-Well}, title = {Uncertainty quantification of wet clutch actuator behaviors in P2 hybrid engine restart process}, booktitle = {SAE Technical Paper}, year = {2022}, volume = {1}, articleno = {2022-01-0652}, doi = {10.4271/2022-01-0652}, note = {2022-01-0652} }Advanced features in automotive systems often necessitate the management of complex interactions between subsystems. Existing control strategies are designed for certain levels of robustness, however their performance can unexpectedly deteriorate in the presence of significant uncertainties, resulting in undesirable system behaviors. This limitation is further amplified in systems with complex nonlinear dynamics. Hydro-mechanical clutch actuators are among those systems whose behaviors are highly sensitive to variations in subsystem characteristics and operating environments. In a P2 hybrid propulsion system, a wet clutch is utilized for cranking the engine during an EV-HEV mode switching event. It is critical that the hydro-mechanical clutch actuator is stroked as quickly and as consistently as possible despite the existence of uncertainties. Thus, the quantification of uncertainties on clutch actuator behaviors is important for enabling smooth EV-HEV transitions. In this paper, a predictive hydro-mechanical clutch actuator model is first presented. The equations of motion of the actuator piston include a parametric representation of squeeze film and friction material compression for damping and stiffness effects. The hydraulic line dynamics is modeled with a series of lumped volumes connected through orifices. Clutch torque is computed based on the Coulomb friction assumption. The model behaviors are qualitatively validated with experimental vehicle data. Monte Carlo simulations are conducted to investigate the effects of uncertainties in the input signal, bulk modulus of the fluid, piston seal friction, and piston damping. The mean behavior of piston pressure changes considerably when the presence of uncertainty is accounted for, which significantly affects the piston motion and clutch torque predictions. The results demonstrate that uncertainty quantification offers valuable insights into system behaviors that are not obtainable through conventional deterministic analyses. This knowledge of the uncertainty propagation can in turn help improve system performance through uncertainty-aware control and hardware design.
@inproceedings{galioto2021_l4dc_objective_partially_observed_lti, author = {Galioto, Nicholas and Gorodetsky, Alex A.}, title = {A new objective for identification of partially observed linear time-invariant dynamical systems from input-output data}, booktitle = {Learning for Dynamics and Control}, year = {2021}, url = {http://proceedings.mlr.press/v144/galioto21a/galioto21a.pdf} }In this work we consider the identification of partially observed dynamical systems from a single trajectory of arbitrary input-output data. We propose a new optimization objective, derived as a MAP estimator of a certain posterior, that explicitly accounts for model, measurement, and parameter uncertainty. This algorithm identifies a linear time invariant model on a hidden latent space of pre-specified dimension. In contrast to Markov-parameter based least squares approaches, our algorithm can be applied to systems with arbitrary forcing and initial conditions, and we empirically show several magnitude improvement in prediction quality compared to state-of-the-art approaches on both linear and nonlinear systems. Furthermore, we theoretically demonstrate how these existing approaches can be derived from simplifying assumptions on our system that neglect the possibility of model errors.
@inproceedings{ji2021_time_delay_bayesian_inference, author = {Ji, Xunbi A. and Molnar, Tamas G. and Gorodetsky, Alex A. and Orosz, Gabor}, title = {Bayesian inference for time delay systems with application to connected automated vehicles}, booktitle = {IEEE International Intelligent Transportation Systems Conference}, year = {2021}, pages = {3259-3264}, doi = {10.1109/ITSC48978.2021.9564457} }In this paper, a Bayesian inference problem is set up to infer the time delay and the resistance models from the dynamics of a connected automated vehicle. The delayed rejection adaptive Metropolis Markov chain Monte Carlo method is applied to obtain the posterior distributions of time delay and resistance parameters simultaneously using experimental data. The estimations of the time delay are shown to be consistent among multiple datasets and different resistance models. The distribution of the posterior indicates that there exist multiple modes in time delay, corresponding to different behaviors in acceleration and deceleration.
@inproceedings{chen2021_behavioral_cloning_atari, author = {Chen, Brian and Tandon, Siddhant and Gorsich, David J. and Gorodetsky, Alex A. and Veerapaneni, Shravan}, title = {Behavioral cloning in Atari games using a combined variational autoencoder and predictor model}, booktitle = {IEEE Conference on Evolutionary Computation}, year = {2021}, pages = {2077-2084}, doi = {10.1109/CEC45853.2021.9505001} }We explore an approach to behavioral cloning in video games. We are motivated to pursue a learning architecture that is data efficient and provides opportunity for interpreting player strategies and replicating player actions in unseen situations. To this end, we have developed a generative model that learns latent features of a game that can be used for training an action predictor. Specifically, our architecture combines a Variational Autoencoder with a discriminator mapping the latent space to action predictions. We compare our model performance to two different behavior cloning architectures: a discriminative model, a Convolutional Neural Network, mapping game states directly to actions, and a Variational Autoencoder with a predictor trained separately. Finally, we demonstrate how we can use the advantage of generative modeling to sample new states from the latent space of the Variational Autoencoder to analyze player actions and provide meaning to certain latent features.
@inproceedings{yang2021_multifidelity_online_propulsion_idetc, author = {Yang, Hang and Gorodetsky, Alex A. and Fujii, Yuji and Wang, Kon-Well}, title = {Multifidelity uncertainty quantification for online simulations of automotive propulsion systems}, booktitle = {ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference}, year = {2021}, articleno = {V009T09A043}, doi = {10.1115/DETC2021-67585} }The increasing complexity and demanding performance requirement of modern automotive propulsion systems necessitate more intelligent and robust predictive controls. Due to the significant uncertainties from both unavoidable modeling errors and probabilistic environmental disturbances, the ability to quantify the effect of these uncertainties to the system behaviors is of crucial importance to enable advanced control designs for automotive propulsion systems. Furthermore, the quantification of uncertainty must be computationally efficient such that it can be conducted on board a vehicle in real time. However, traditional uncertainty quantification methods for complicated nonlinear systems, such as Monte Carlo, often rely on sampling, a computationally prohibitive process for many applications. Previous research has shown promise in using spectral decomposition methods such as generalized Polynomial Chaos to reduce the online computational cost of uncertainty quantification. However, such methods suffer from scalability and bias issues. This paper seeks to alleviate these computational bottlenecks by developing a multifidelity uncertainty quantification method that combines low-order generalized Polynomial Chaos with Monte Carlo estimation via control variates. Results on the mean and variance estimates of the axle shaft torque show that the proposed method can correct the bias of low-order Polynomial Chaos expansions while significantly reducing variance compared to conventional Monte Carlo.
@inproceedings{gorodetsky2021_robust_design_electrospray_emitters, author = {Gorodetsky, Alex A. and Whittaker, Collin B. and Szulman, Audelia and Jorns, Benjamin A.}, title = {Robust design of electrospray emitters}, booktitle = {AIAA Propulsion and Energy 2021 Forum}, year = {2021}, doi = {10.2514/6.2021-3422} }We utilize the Electrospray Propulsion Engineering Toolkit (ESPET) to perform simulation-based design of electrospray emitters. Our design goals are to achieve robust performance of a geometrically feasible design under uncertainties inherent in manufacturing tolerances, model parameters, and operating conditions. We first describe our modeling approach by deriving and justifying geometric, operational, and performance constraints that define a feasible design. We then describe the uncertainties with respect to which we seek robustness. Finally, we describe a rejection sampling algorithm to automate the process of obtaining feasible robust designs that meet constraints with 95\\% probability. The resulting feasible design space is shown to be smaller and more constrained than designs which meet constraints at fixed, nominal parameter settings.
@inproceedings{galioto2020_hamiltonian_dynamics_symplectic_data, author = {Galioto, Nicholas and Gorodetsky, Alex A.}, title = {Bayesian identification of Hamiltonian dynamics from symplectic data}, booktitle = {IEEE Conference on Decision and Control}, year = {2020}, pages = {1190-1195}, doi = {10.1109/CDC42340.2020.9303852} }We propose a Bayesian probabilistic formulation for system identification of Hamiltonian systems. This approach uses an approximate marginal Markov Chain Monte Carlo algorithm to directly discover a system Hamiltonian from data. Our approach improves upon existing methods in two ways: first we encode the fact that the data generating process is symplectic directly into our learning objective, and second we utilize a learning objective that simultaneously accounts for unknown parameters, model form, and measurement noise. This objective is the log marginal posterior of a probabilistic model that embeds a symplectic and reversible integrator within an uncertain dynamical system. We demonstrate that the resulting learning problem yields dynamical systems that have improved accuracy and reduced predictive uncertainty compared to existing state-of-the-art approaches. Simulation results are shown on the Henon-Heiles Hamiltonian system.
@inproceedings{whittaker2020_scaling_laws_electrospray, author = {Whittaker, Collin B. and Gorodetsky, Alex A. and Jorns, Benjamin A.}, title = {Quantifying uncertainty in the scaling laws of porous electrospray emitters}, booktitle = {AIAA Propulsion and Energy 2020 Forum}, year = {2020}, doi = {10.2514/6.2020-3615} }Uncertainty in the model parameters of several scaling laws applicable to porous electrosprays is quantified using Bayesian inference. Specifically, models describing ion current in the pure-ionic regime, jet current in the cone-jet regime, and the number of active emitter sites as a function of applied voltage are examined. Data from previously published experimental studies are used to generate posterior distributions of the model parameters. Different assignments for the uncertainty are considered where unavailable from empirical estimates. These distributions are then used in combination with the Electrospray Propulsion Engineering Toolkit (ESPET) QuickSolver to generate performance predictions with confidence intervals for a real porous emitter. The results of these analyses are compared to previously given values for the model parameters and experimental data external to the inference. The model parameters are found to be well determined by the data, with full widths at half maxima 1-2 orders of magnitude below their peaks. Predictions incorporating the posteriors are found not to agree the external data, and a lack of applicability of the ionic current model is examined as a cause. In light of this disagreement, the external data is incorporated to update the posteriors, and it is found that the ionic current scaling changes much more significantly than the other parameters, identifying it as the primary source of disagreement. These results are discussed within the context of additional model development and the extension of this framework to support robust, model-based design.
@inproceedings{baskar2020_simulated_wind_field_dataset, author = {Baskar, Deepika and Gorodetsky, Alex A.}, title = {Simulated wind-field dataset for testing energy efficient path-planning algorithms for UAVs in urban environment}, booktitle = {AIAA Aviation Forum}, year = {2020}, doi = {10.2514/6.2020-2920} }Managing winds in the urban wind environment is an important aspect for enabling efficient wide-spread autonomous drone activity in urban centers. Literature studying the effects of wind on urban air mobility in a realistic urban geometry is emerging and typically requires comprehensive fluid dynamics simulations. However, the accessibility of these approaches to those with less fluid dynamics experience and/or without access to purpose built simulation tools has limited validation and application of the corresponding results. This paper seeks to address this issue by describing a set of wind simulations in a real urban environment that we have made openly available to the community. Our aim is to increase the feasibility of using fluid dynamics simulation for testing UAV strategies in the urban environment. As an example application, we use our dataset to determine energy optimal paths for a hypothetical fixed-wing UAV tasked with making trips spanning a few city blocks. We demonstrate that energy efficiency considerations can indeed lead to different path planning results than those used by conventional shortest path planners, and therefore may be an important factor when designing UAV operations.
@inproceedings{he2020_dynamic_soaring_tracking_uq, author = {He, Kaijun and Wang, Jiachen and Gorodetsky, Alex A.}, title = {Uncertainty analysis of trajectory tracking for autonomous dynamic soaring}, booktitle = {AIAA SCITECH 2020 Forum}, year = {2020}, doi = {10.2514/6.2020-0908} }We quantify the effect of mis-modeled wind conditions on planned and executed energy-neutral trajectories for autonomous dynamic gliding aircraft with a sampling-based probabilistic assessment. Our conclusions indicate the need for future approaches to incorporate model-form error of the wind dynamics into adaptive and/or feedback controllers. While previous works have either analyzed the uncertainty in open-loop controllers developed through either deterministic or stochastic (robust) optimization, our analysis considers the performance of closed-loop (reference-tracking) controllers in the context of both parameter and model-form errors. These controllers use a forward-looking model predictive controller to track a trajectory that was optimized for a deterministic wind profile. The performance of the glider was then simulated using different deterministic wind profiles and gust conditions. The total air-relative energy and glider displacement were then measured for each wind realization to determine the effect of wind field uncertainty on performance. We conclude that the closed-loop controller can efficiently improve the trajectory tracking performance if the deterministic wind profile is not very different from the predicted wind model. However, the closed-loop performance under significant difference in the model form of the wind profile was far from optimal. We find that mis-modelling the underlying deterministic wind profile causes up to 30\% loss in energy, significantly more than any effects due to gust.
@inproceedings{yang2020_gpc_online_propulsion_acc, author = {Yang, Hang and Kidambi, Narayanan and Fujii, Yuji and Gorodetsky, Alex A. and Wang, Kon-Well}, title = {Uncertainty quantification using generalized polynomial chaos for online simulations of automotive propulsion systems}, booktitle = {American Control Conference}, year = {2020}, pages = {295-300}, doi = {10.23919/ACC45564.2020.9147870} }Online simulations conducted in vehicles can enable predictive control of automotive systems. This capability can be especially valuable for complex propulsion systems to manage performance, safety, and efficiency under changing drive conditions. Reliable online simulations require accurate models. However, modeling errors are unavoidable, and the inputs from the driver and environment are subject to uncertainty and generally unknown a priori, rendering the system stochastic. Furthermore, limited computing resources in a vehicle can prohibit solving stochastic systems, posing a major challenge. This paper seeks to alleviate these computational bottlenecks by utilizing generalized polynomial chaos to efficiently propagate and quantify uncertainty without loss of accuracy for online propulsion system simulations. To demonstrate the effectiveness of this method, uncertainty quantification is performed for simulations of vehicle launch where both model and input uncertainties are considered. A standard Monte Carlo method is used as a baseline for comparison. It is shown that, for the same accuracy, the proposed method is more than two orders of magnitude faster than a Monte Carlo method. A variance-based sensitivity analysis is also used to quantify the statistical contribution from each uncertainty source to the output. The outcome suggests that the proposed method is well-suited to automotive applications where fast and accurate on-board simulation capabilities are required.
@inproceedings{geraci2019_recent_advancements_sequoia, author = {Geraci, Gianluca and Eldred, Michael S. and Gorodetsky, Alex A. and Jakeman, John D.}, title = {Recent advancements in multilevel-multifidelity techniques for forward UQ in the DARPA SEQUOIA project}, booktitle = {AIAA SCITECH 2019 Forum}, year = {2019}, doi = {10.2514/6.2019-0722} }In the context of the DARPA funded project SEQUOIA we are interested in the design under uncertainty of a jet engine nozzle subject to the performance requirements of a reconnaissance mission for a small unmanned military aircraft. This design task involves complex and expensive aero-thermo-structural computational analyses where it is of paramount importance to also include the effect of uncertain variables to obtain reliable predictions of the device's performance. In this work we focus on the forward propagation analysis which is a key part of the design under uncertainty workflow. This task cannot be tackled directly by means of single-fidelity approaches due to the prohibitive computational cost associated to each realization. We report here a summary of our latest advancement regarding several multilevel and multifidelity strategies designed to alleviate these challenges. The overall goal of these techniques is to reduce the computational cost of analyzing a high-fidelity model by resorting to less accurate, but less computationally demanding, lower-fidelity models. The features of these multifidelity uncertainty quantification approaches are initially illustrated and demonstrated on several model problems and afterward for the aero-thermo-structural analysis of the jet engine nozzle.
@inproceedings{jorns2019_electrospray_array_lifetime_uq, author = {Jorns, Benjamin A. and Gorodetsky, Alex A. and Lasky, Ian and Kimber, Angela and Dahl, Peter and St. Peter, Benjamin and Dressler, Rainer A.}, title = {Uncertainty quantification of electrospray thruster array lifetime}, booktitle = {International Electric Propulsion Conference}, year = {2019}, url = {http://electricrocket.org/2019/317.pdf}, note = {IEPC-2019-317} }A numerical investigation into the performance and lifetime of an electrospray array thruster of pressurized-capillary emitters is presented. A series of modules based on the Electrospray Propulsion Engineering Toolkit (ESPET) are employed to create a reduced-fidelity model for the operation of a colloidal thruster. New modules are added to this toolkit to enable predictions of lifetime including scaling laws for beam divergence, propellant deposition on the extractor grid, and failure due to backstreaming current. The impact of uncertainty on performance and lifetime is also quantified. Sources of uncertainty considered include both physics-based model parameters and manufacturing tolerances. A Monte Carlo analysis is applied to generate probability distribution functions for key performance parameters including thrust, efficiency, and specific impulse. The median performance values are shown to agree qualitatively with typical performance conditions for this pressure-fed configuration of an electrospray array. Probability of failure curves are also generated for both a single emitter and an array of emitters operated on the same power supply. It is found that as the uncertainty in design parameters or the number of emitters increases, the lifetime of the array decreases. Parametric analyses are also performed with the goal to optimize thruster performance while accounting for uncertainty. To this end, it is shown that there is an optimum throttling point for achieving maximum predicted total impulse. This proof of concept thus illustrates the potential capability of this approach for guiding design and optimization.
@inproceedings{tal2018_zero_sum_differential_games, author = {Tal, Ezra and Gorodetsky, Alex A. and Karaman, Sertac}, title = {Continuous tensor train-based dynamic programming for high-dimensional zero-sum differential games}, booktitle = {American Control Conference}, year = {2018}, pages = {6086-6093}, doi = {10.23919/ACC.2018.8431472} }Zero-sum differential games constitute a prominent research topic in several fields ranging from economics to motion planning. Unfortunately, analytical techniques for differential games can address only simple, illustrative problem instances, and most existing computational methods suffer from the curse of dimensionality, i.e., the computational requirements grow exponentially with the dimensionality of the state space. In order to alleviate the curse of dimensionality for a certain class of two-player pursuit-evasion games, we propose a novel dynamic-programming-based algorithm that uses a continuous tensor-train approximation to represent the value function. In this way, the algorithm can represent high-dimensional tensors using computational resources that grow only polynomially with dimensionality of the state space and with the rank of the value function. The proposed algorithm is shown to converge to optimal solutions. It is demonstrated in several problem instances; in case of a seven-dimensional game, the value function representation was obtained with seven orders of magnitude savings in computational and memory cost, when compared to standard value iteration.
@inproceedings{geraci2018_active_subspaces_multifidelity, author = {Geraci, Gianluca and Eldred, Michael S. and Gorodetsky, Alex A. and Jakeman, John D.}, title = {Leveraging active subspaces for efficient multifidelity uncertainty quantification}, booktitle = {ECCM-ECCFD 2018}, year = {2018}, url = {https://congress.cimne.com/eccm_ecfd2018/admin/files/filePaper/p1481.pdf} }In this work, we focus on sampling-based methods for forward uncertainty propagation, and in particular, on multifidelity sampling methods that employ a control variate approach. The novel component of this work is to accelerate the sampling by relying on important directions, as for instance in Active Subspaces. The idea consists of discovering the important directions for each model in order to provide a reduced dimensional link between the parameterization of each model fidelity and the relevant quantities of interest. This accomplishes two goals: (i) enhancing the correlation between models, and (ii) providing a mechanism to effectively bridge dissimilar input parameterizations. We demonstrate the performance of our approach for two model problems.
@inproceedings{eldred2018_multilevel_multifidelity_sequoia, author = {Eldred, Michael S. and Geraci, Gianluca and Gorodetsky, Alex A. and Jakeman, John D.}, title = {Multilevel-multifidelity approaches for forward UQ in the DARPA SEQUOIA project}, booktitle = {AIAA Non-Deterministic Approaches Conference}, year = {2018}, doi = {10.2514/6.2018-1179} }Within the SEQUOIA project, funded by the DARPA EQUiPS program, we pursue algorithmic approaches that enable comprehensive design under uncertainty, through inclusion of aleatory or parametric and epistemic or model-form uncertainties within scalable forward and inverse uncertainty quantification approaches. These statistical methods are embedded within design processes that manage computational expense through active subspace, multilevel-multifidelity, and reduced-order modeling approximations. To demonstrate these methods, we focus on the design of devices that involve multiphysics interactions in advanced aerospace vehicles. A particular problem of interest is the shape design of nozzles for advanced vehicles such as the Northrop Grumman UCAS X-47B, involving coupled aero-structural-thermal simulations for nozzle performance. In this paper, we explore a combination of multilevel and multifidelity forward and inverse uncertainty quantification algorithms to reduce the overall computational cost of the analysis by leveraging hierarchies of model form and solution discretization in order to exploit tradeoffs between solution accuracy and cost. In particular, we seek the most cost-effective fusion of information across complex multidimensional modeling hierarchies. Results to date indicate the utility of multiple approaches, including methods that optimally allocate resources when estimator variance varies smoothly across levels, methods that allocate sufficient sampling density based on sparsity estimates, and methods that employ greedy multilevel refinement.
@inproceedings{gorodetsky2017_low_rank_tensor_integration_filtering, author = {Gorodetsky, Alex A. and Karaman, Sertac and Marzouk, Youssef M.}, title = {Low-rank tensor integration for Gaussian filtering of continuous time nonlinear systems}, booktitle = {IEEE Conference on Decision and Control}, year = {2017}, pages = {2789-2794}, doi = {10.1109/CDC.2017.8264064} }Integration-based Gaussian filters such as unscented, cubature, and Gauss-Hermite filters are effective ways to assimilate data and models within nonlinear systems. Traditionally, these filters have only been applicable for systems with a handful of states due to stability and scalability issues. In this paper, we present a new integration method for scaling quadrature-based filters to higher dimensions. Our approach begins by decomposing the dynamics and observation models into separated, low-rank tensor formats. Once in low-rank tensor format, adaptive integration techniques may be used to efficiently propagate the mean and covariance of the distribution of the system state with computational complexity that is polynomial in dimension and rank. Simulation results are shown on nonlinear chaotic systems with 20 state variables.
@inproceedings{alora2016_low_rank_control_systems_scltl, author = {Alora, John Irvin and Gorodetsky, Alex A. and Karaman, Sertac and Marzouk, Youssef M. and Lowry, Nathan}, title = {Automated synthesis of low-rank control systems from sc-LTL specifications using tensor-train decompositions}, booktitle = {IEEE Conference on Decision and Control}, year = {2016}, pages = {1131-1138}, doi = {10.1109/CDC.2016.7798419} }Correct-by-design automated construction of control systems has attracted a tremendous amount of attention. However, most existing algorithms for automated construction suffer from the curse of dimensionality, i.e., their run time scales exponentially with increasing dimensionality of the state space. As a result, typically, systems with only a few degrees of freedom are considered. In this paper, we propose a novel algorithm based on the tensor-train decomposition that solves stochastic optimal control problems with syntactically co-safe linear temporal logic specifications. We show that, under certain conditions, the run time of the proposed algorithm scales polynomially with the dimensionality of the state space and the rank of the optimal cost-to-go function. We demonstrate the algorithm in a six-dimensional problem instance involving a simple airplane model. In this example, the proposed algorithm provides up to four orders of computational savings when compared to the standard value iteration algorithm.
@inproceedings{gorodetsky2015_stochastic_optimal_motion_control_rss, author = {Gorodetsky, Alex A. and Karaman, Sertac and Marzouk, Youssef M.}, title = {Efficient high-dimensional stochastic optimal motion control using tensor-train decomposition}, booktitle = {Robotics: Science and Systems}, year = {2015}, doi = {10.15607/RSS.2015.XI.015} }Stochastic optimal control problems frequently arise as motion control problems in the context of robotics. Unfortunately, all existing approaches that guarantee arbitrary precision suffer from the curse of dimensionality: the computational effort invested by the algorithm grows exponentially fast with increasing dimensionality of the state space of the underlying dynamic system governing the robot. In this paper, we propose a novel algorithm that utilizes compressed representations to efficiently solve stochastic optimal control problems with arbitrary precision. The running time of the new algorithms scales linearly with increasing dimensionality of the state space. The running time also depends polynomially on the rank of the value function, a measure that quantifies the intrinsic geometric complexity of the value function, due to the geometry and physics embedded in the problem instance at hand. The new algorithms are based on recent analysis and algorithms for tensor decomposition, generalizing matrix decomposition algorithms, e.g. the singular value decomposition, to three or more dimensions. In computational experiments, we show the computational effort of the new algorithm also scales linearly with the discretization resolution of the state space. We also demonstrate the new algorithm on a problem involving the perching of an aircraft, represented by a nonlinear non-holonomic longitudinal model with a seven-dimensional state space, the full numerical solution to which was not obtained before. In this example, we estimate that the proposed algorithm runs more than seven orders of magnitude faster, when compared to naive value iteration.
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Theses
@phdthesis{aksoy2025_umich_phd, author = {Aksoy, Doruk}, title = {Incremental tensor decompositions for scientific machine learning and Bayesian inference}, school = {University of Michigan}, year = {2025}, doi = {10.7302/28229}, url = {https://hdl.handle.net/2027.42/201145} }This thesis addresses the fundamental challenges of processing large-scale, high-dimensional data frequently arising in machine learning and scientific computing. It focuses on developing novel incremental tensor decomposition algorithms that enable efficient processing of high-dimensional data streams and large-scale stationary datasets. This work is motivated by the necessity for scalable dimensionality-reduction techniques that can provide an error-bounded approximation of high-dimensional data while providing a useful low-dimensional representation for downstream tasks such as Bayesian inference, behavioral cloning, and generative modeling. As modern scientific simulations and data acquisition systems generate multidimensional datasets at unprecedented scales, ranging from terabytes in computational fluid dynamics to petabytes in atmospheric reanalysis, traditional dimensionality-reduction methods fail to accommodate the streaming nature and memory constraints of these applications. On the other hand, large-scale machine-learning models such as large language models and foundational models, which are trained on massive datasets, require efficient data-representation techniques to reduce storage and computational costs while preserving essential data characteristics. This thesis presents three novel algorithms for computing tensor decompositions: the Tensor-Train Incremental Core Expansion algorithm is an incremental algorithm for updating an existing approximation of tensors in tensor-train format when new tensors become available, the Batch Hierarchical Tucker leaves-to-root algorithm computes an approximation of a batch of tensors in batch-modified hierarchical Tucker format, and the Hierarchical Tucker Rapid Incremental Subspace Expansion algorithm is another incremental algorithm for updating an existing approximation of tensors in batch hierarchical Tucker format. These algorithms are designed to overcome the limitations of existing approaches by providing theoretical guarantees on the approximation error, enabling downstream applications, providing support for data streams, and preserving the high-dimensional structure of the data. The effectiveness of these methods is demonstrated across diverse applications in scientific computing and machine learning. For scientific data, Tensor-Train Incremental Core Expansion achieves compression ratios up to 300,000x on particle-in-cell simulations to increase storage efficiency. It also provides compression ratios up to 32.8x on chaotic partial-differential-equation based simulations of a sheet of self-oscillating gels while preserving reconstruction quality suitable for Bayesian inversion. For image and video data, Hierarchical Tucker Rapid Incremental Subspace Expansion offers on-disk compression performance comparable to JPEG encoding while maintaining the perceptual structure of the images. This enables effective downstream applications including behavioral cloning with 2.6x to 9.6x training speedup and generative modeling through diffusion models. This thesis demonstrates that tensor-network embeddings can serve as powerful dimensionality-reduction tools that preserve essential data characteristics while dramatically reducing storage and computational requirements. These findings contribute to scientific machine learning and high-dimensional data analysis by providing scalable algorithms that democratize access to advanced machine-learning techniques for resource-constrained environments and enable real-time processing of streaming high-dimensional data. The developed methods open new possibilities for online learning, incremental model updates, and efficient data representation in scientific computing and artificial intelligence applications.
@phdthesis{chen2024_umich_phd, author = {Chen, Brian}, title = {Applications of generative models and tensor networks for neural quantum states and imitation learning}, school = {University of Michigan}, year = {2024}, doi = {10.7302/25002}, url = {https://hdl.handle.net/2027.42/196066} }Recently developed tools such as neural-network based generative models and incremental tensor networks are promising methods for simplifying the learning of functions in high-dimensional space. We consider the application of these tools in two particular areas: modeling quantum states and imitation learning from high-dimensional data. In the first application, we consider the use of generative models such as normalizing flows as neural quantum states. Because quantum states are functions $\psi$ such that $|\psi|^2$ is a probability density, using normalizing flows as neural quantum states is a natural choice. Neural quantum states are commonly used in Variational Monte Carlo, where the parameters $\theta$ of a parameterized quantum state $\psi_\theta$ are varied in order to minimize some objective function. Due to the ability to exactly sample from and estimate probability densities from normalizing flows, the use of normalizing flows as neural quantum states simplifies the calculation of integrals used in Variational Monte Carlo. This is applied in two settings: first we consider using Variational Monte Carlo for minimizing the ground state energy of high-dimensional continuous quantum states. Second, we explore using Variational Monte Carlo for numerically solving time-dependent partial differential equations. For the second application, we explore using generative models and incremental tensor networks for extracting a low-dimensional latent space for use in downstream tasks like imitation learning. We first explore the use of neural-network architectures like Variational Autoencoders for learning a latent space that can be sampled from. Doing this allows for synthetic states to be generated, as well as predicted actions for those states. However, the use of these neural-network based feature extractors can be expensive, due to hyperparameter tuning and the gradient-based optimization methods used to find a good latent-space representation. We explore the use of incremental tensor-network approaches, which can extract a latent space in one pass through the training data and require minimal hyperparameter tuning. We find that these incremental tensor-network approaches learn a latent-space representation that leads to similar imitation-learning accuracy, but provides significant computational speedups over the neural-network approaches.
@phdthesis{galioto2023_umich_phd, author = {Galioto, Nicholas}, title = {Generalization of system identification objective functions through stochastic hidden Markov models for regularization, smoothness, and uncertainty quantification}, school = {University of Michigan}, year = {2023}, url = {https://hdl.handle.net/2027.42/177756} }With the growing availability of computational resources, the interest in learning models of dynamical systems has grown exponentially over the years across many diverse disciplines. As a result of this growth, objective functions for model estimation have been rapidly developed independently across fields such as fluids, control, and machine learning. Theoretical justifications for these objectives, however, have lagged behind. In this dissertation, we provide a unifying theoretical framework for some of the most popular of these objectives, specifically dynamic mode decomposition, single rollout Markov parameter estimation, sparse identification of nonlinear dynamics, and multiple shooting. In this framework, we model a general dynamical system using a hidden Markov model and derive a marginal likelihood that can be used for estimation. The key difference between this and most existing likelihood estimators is that rather than simply modeling the estimation error in the output of the system, we additionally model the error in the dynamics through the inclusion of a process noise term. Not only does this process noise term provide the flexibility needed to generalize many existing objectives, but it also provides three significant advantages in the marginal likelihood. The first is that it generates an explicit regularization term that arises directly from the model formulation without the need for adding heuristic priors onto the parameters. Furthermore, this regularization term is over the output, rather than the parameters, of the model and is therefore applicable to any arbitrary parameterization of the dynamics. Secondly, the process noise term provides smoothing of the marginal likelihood optimization surface without having to discount the information in the data through tempering methods or abbreviated simulation lengths. Lastly, estimation of the process noise term can give a quantification of the uncertainty of the estimated model without necessarily requiring expensive Markov chain Monte Carlo sampling. To evaluate this proposed marginal likelihood, we present an efficient recursive algorithm for linear-Gaussian models and an approximation to this algorithm for all remaining models. We discuss how simplifications to the approximate algorithm can be made when the noise is additive Gaussian and derive simplifications for when it is arbitrary additive or multiplicative noise. Next, we provide theoretical results proving that the considered objectives are special cases of a posterior that uses the proposed marginal likelihood. These results uncover the sets of assumptions needed to transform the negative log posterior into each of the objective functions that we consider. We then present numerical experiments that compare the approximate marginal likelihood to each of the considered objectives on a variety of systems. These experiments include linear, chaotic, partial differential equation, limit cycle, and Hamiltonian systems. Additionally, we include a novel comparison of Hamiltonian estimation using symplectic and non-symplectic dynamics propagators. This comparison uses uncertainty quantification both in the form of Markov chain Monte Carlo sampling and process noise covariance estimation to show that embedding the symplectic propagator into the objective delivers more precise estimates than embedding the objective with the non-symplectic propagator. Overall, the results of this dissertation demonstrate that the marginal likelihood is able to produce more accurate estimates on problems with high amounts of uncertainty in the forms of measurement noise, measurement sparsity, and model expressiveness than comparable objective functions.
@phdthesis{yang2022_umich_phd, author = {Yang, Hang}, title = {A surrogate-based variance reduction approach to multifidelity uncertainty quantification --- with applications to automotive systems}, school = {University of Michigan}, year = {2022}, url = {https://hdl.handle.net/2027.42/172606} }An increasing number of science and engineering applications demand highly efficient uncertainty quantification capabilities in order to account for the presence of significant uncertainties that are often unavoidable in real-world operating conditions. For complex nonlinear systems, the task of quantifying the effect of uncertainties on system behaviors can pose major challenges as closed-form solutions to the stochastic nonlinear differential equations often do not exist. Sampling-based algorithms, most notably the Monte Carlo method, are considered the default approach when it comes to uncertainty quantification for complex nonlinear systems. However, Monte Carlo relies on repeated random sampling and simulations to obtain statistical estimations, which has very slow convergence. The resulting computational cost is often prohibitively high for complex nonlinear systems, hindering the adoption of such uncertainty analyses in many applications where computational resources are constrained. This dissertation research investigates surrogate-based single-fidelity and multifidelity methods for highly efficient uncertainty quantification. We first demonstrate the performance improvement obtained by the employment of generalized Polynomial Chaos as a surrogate in the uncertainty quantification of automotive propulsion system simulations. The adoption of generalized Polynomial Chaos enables the exploitation of the smoothness property of the solution to the stochastic problem for significant computational cost reductions. Based upon this surrogate approach, we further develop a novel multifidelity variance reduction method for highly efficient forward uncertainty quantification for systems with limited computational budgets. Our proposed method, Control Variate Polynomial Chaos, utilizes Control Variate as an information-fusion framework to explore synergies between the flexible Monte Carlo sampling and the efficient generalized Polynomial Chaos expansion, while minimizing the drawbacks of both individual techniques. Specifically, a high-fidelity model of the system of interest is utilized in a Monte Carlo sampling scheme to form the high-fidelity component of a Control Variate Polynomial Chaos estimator. A surrogate model obtained using a low-degree generalized Polynomial Chaos expansion is employed in the low-fidelity component of the Control Variate Polynomial Chaos estimator. The generalized Polynomial Chaos coefficients are then fused with random samples of the polynomial bases to complete the low-fidelity component of the Control Variate Polynomial Chaos estimator. The same set of random samples are shared between the high- and low-fidelity components to generate correlations. Finally, the high- and low-fidelity components are combined through control variates to achieve variance reductions. The primary theoretical contribution of this dissertation is the rigorous development of an estimator design strategy that optimally balances the computational effort needed to adapt a surrogate compared with sampling the original expensive nonlinear system. While previous works in the literature have similarly combined surrogates and sampling, to the author's best knowledge, this dissertation work is the first to provide rigorous analysis of estimator design. Numerical results from multiple application examples show that Control Variate Polynomial Chaos can produce significant, often by orders of magnitude, computational efficiency improvement over existing uncertainty quantification methods. The main contributions of this dissertation include: 1) application of generalized Polynomial Chaos to efficient uncertainty quantification and global sensitivity analysis for the online simulations of automotive propulsion systems; 2) development of theoretical foundations for the Control Variate Polynomial Chaos method; 3) development of the optimal estimator design theory for Control Variate Polynomial Chaos; and 4) numerical applications of optimal Control Variate Polynomial Chaos. The results show that Control Variate Polynomial Chaos can provide significant, often by orders of magnitude, computational cost reductions over conventional uncertainty quantification methods without sacrificing accuracy.
@phdthesis{gorodetsky2017_mit_phd, author = {Gorodetsky, Alex A.}, title = {Continuous low-rank tensor decompositions, with applications to stochastic optimal control and data assimilation}, school = {Massachusetts Institute of Technology}, year = {2017}, url = {http://hdl.handle.net/1721.1/108918} }Optimal decision making under uncertainty is critical for control and optimization of complex systems. However, many techniques for solving problems such as stochastic optimal control and data assimilation encounter the curse of dimensionality when too many state variables are involved. In this thesis, we propose a framework for computing with high-dimensional functions that mitigates this exponential growth in complexity for problems with separable structure. Our framework tightly integrates two emerging areas: tensor decompositions and continuous computation. Tensor decompositions are able to effectively compress and operate with low-rank multidimensional arrays. Continuous computation is a paradigm for computing with functions instead of arrays, and it is best realized by Chebfun, a MATLAB package for computing with functions of up to three dimensions. Continuous computation provides a natural framework for building numerical algorithms that effectively, naturally, and automatically adapt to problem structure. The first part of this thesis describes a compressed continuous computation framework centered around a continuous analogue to the discrete tensor-train decomposition called the function-train decomposition. Computation with the function-train requires continuous matrix factorizations and continuous numerical linear algebra. Continuous analogues are presented for performing cross approximation, rounding, multilinear algebra operations such as addition, multiplication, integration, and differentiation, and continuous, rank-revealing, alternating least squares. Advantages of the function-train over the tensor-train include the ability to adaptively approximate functions and the ability to compute with functions that are parameterized differently. For example, while elementwise multiplication between tensors of different sizes is undefined, functions in function-train format can be readily multiplied together. Next, we develop compressed versions of value iteration, policy iteration, and multilevel algorithms for solving dynamic programming problems arising in stochastic optimal control. These techniques enable computing global solutions to a broader set of problems, for example those with non-affine control inputs, than previously possible. Examples are presented for motion planning with robotic systems that have up to seven states. Finally, we use the function-train to extend integration-based Gaussian filtering to larger state spaces than previously considered. Examples are presented for dynamical systems with up to twenty states.
@mastersthesis{gorodetsky2012_mit_sm, author = {Gorodetsky, Alex A.}, title = {A learning method for the approximation of discontinuous functions for stochastic simulations}, school = {Massachusetts Institute of Technology}, year = {2012}, url = {http://hdl.handle.net/1721.1/76101} }Surrogate models for computational simulations are inexpensive input-output approximations that allow expensive analyses, such as the forward propagation of uncertainty and Bayesian statistical inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, however, most existing surrogate-construction methodologies yield large errors and slow convergence rates. This thesis develops a new methodology for approximating simulation outputs that depend discontinuously on input parameters. Our approach focuses on piecewise smooth outputs and involves two stages: first, efficient detection and localization of discontinuities in high-dimensional parameter spaces using polynomial annihilation, support vector machine classification, and uncertainty sampling; second, approximation of the output on each region using Gaussian process regression. The discontinuity-detection methodology is illustrated on examples of up to 11 dimensions, including algebraic models and ordinary differential equation systems, demonstrating improved scaling and efficiency over other methods found in the literature. Finally, the complete surrogate-construction approach is demonstrated on two physical models exhibiting canonical discontinuities: shock formation in Burgers' equation and autoignition in hydrogen-oxygen combustion.
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Preprints
@misc{galioto2026_arch3d, author = {Galioto, Nicholas and Stansbury, Cooper and Gorodetsky, Alex A. and Rajapakse, Indika}, title = {ARCH3D: a foundation model for global genome architecture}, howpublished = {bioRxiv preprint}, year = {2026}, url = {https://www.biorxiv.org/content/10.64898/2026.02.23.707580.abstract}, note = {bioRxiv preprint} }Biological foundation models are transforming scientific discovery by creating information-rich representations that enable inference in low-data settings. Progress on these models has mainly been achieved by increasing input contextual information, for example base pairs or genes. Most work, however, focuses on DNA, RNA, and protein, leaving genome architecture, a fundamental component regulating processes like the cell cycle and cell-fate determination, underexplored. Here, we introduce ARCH3D: a foundation model for global genome architecture. ARCH3D uses a novel masked locus modeling task that increases input contextual information to include genome-wide contact profiles of loci spread across the entirety of the genome. We demonstrate this strategy captures global genome structure by showing ARCH3D embeddings preserve genomic spatial structure, reconstruct interchromosomal interactions under extreme sparsity, and enable identification of multi-way interactions. Ultimately, ARCH3D provides a potential structural foundation for building the virtual genome, an artificial intelligence-based model capable of simulating genome behavior and dynamics.
@misc{gorodetsky2026_block_adaptive_trt, author = {Gorodetsky, Alex A. and Mullen, Patrick D. and Deshpande, Aditya S. and Dolence, Joshua C. and Meyer, Chad D. and Miller, Jonah M. and Roberts, Luke F.}, title = {Tensor networks for block adaptive thermal radiation transport}, howpublished = {Preprint}, year = {2026}, note = {Preprint} }Thermal radiation transport requires solving high-dimensional partial differential equations, while realistic problems couple thermal radiation transport with hydrodynamics and therefore require localized mesh refinement. Existing low-rank and tensor approaches exploit separability, but they do not accommodate block-adaptive refinement and conservative inter-block communication. Moreover, existing mesh refinement schemes exploit locality, but they do not reduce the expense of solving the high-dimensional partial differential equations. This paper introduces a framework to combine these aspects through block-local tensor-train representations of the photon specific intensity that exploit both spatial locality and global separability. Our contributions describe conservative ghost-cell transfer, coarse-fine flux correction, and refinement criteria that balance spatial and rounding error. Numerical experiments demonstrate that adaptive mesh refinement localizes regions with high rank, non-separable structure, achieving compression factors exceeding approximately 10^3. Overall, the presented framework provides a core capability needed to extend tensor-network thermal radiation transport to adaptive-mesh-refinement centered multiphysics settings such as radiation hydrodynamics.
@misc{wang2025_global_lipschitz_bsl, author = {Wang, Liliang and Gorodetsky, Alex A.}, title = {A global Lipschitz stability perspective for understanding approximate approaches in Bayesian sequential learning}, howpublished = {Preprint}, year = {2025}, note = {Preprint} }We establish a general, non-asymptotic error analysis framework for understanding the effects of incremental approximations made by practical approaches for Bayesian sequential learning on their long-term inference performance. Our setting covers inverse problems, state estimation, and parameter-state estimation. In these settings, we bound the difference, termed the learning error, between the unknown true posterior and the approximate posterior computed by these approaches, using three widely used distribution metrics: total variation, Hellinger, and Wasserstein distances. This framework builds on our establishment of the global Lipschitz stability of the posterior with respect to the prior across these settings. To the best of our knowledge, this is the first work to establish such global Lipschitz stability under the Hellinger and Wasserstein distances and the first general error analysis framework for approximate Bayesian sequential learning methods. Our framework offers two sets of upper bounds on the learning error. The first set demonstrates the stability of general approximate Bayesian sequential learning methods with respect to the incremental approximation process, while the second set is estimable in many practical scenarios. Furthermore, as an initial step toward understanding the phenomenon of learning error decay, which is sometimes observed, we identify sufficient conditions under which data assimilation leads to learning error reduction.
@misc{dixon2025_bistro, author = {Dixon, Thomas O. and Bomarito, Geoffrey F. and Warner, James E. and Gorodetsky, Alex A.}, title = {BISTRO: a bi-fidelity stochastic gradient framework using trust-regions for optimization under uncertainty}, howpublished = {arXiv preprint}, year = {2025}, url = {https://arxiv.org/pdf/2512.09055}, note = {arXiv preprint} }Stochastic optimization of engineering systems is often infeasible due to repeated evaluations of a computationally expensive, high-fidelity simulation. Bi-fidelity methods mitigate this challenge by leveraging a cheaper, approximate model to accelerate convergence. Most existing bi-fidelity approaches, however, exploit either design-space curvature or random-space correlation, not both. We present BISTRO, a bi-fidelity stochastic trust-region optimizer for unconstrained optimization under uncertainty through a stochastic approximation procedure. This approach exploits the curvature information of a low-fidelity objective function to converge within a basin of a local minimum of the high-fidelity model where low-fidelity curvature information is no longer valuable. The method then switches to a variance-reduced stochastic gradient descent procedure. We provide convergence guarantees in expectation under certain regularity assumptions and ensure the best-case O(1/n) convergence rate for stochastic optimization. On benchmark problems and a 20-dimensional space shuttle reentry case, BISTRO converges faster than adaptive sampling and variance reduction procedures and cuts computational expense by up to 29x.
@misc{muchandimath2025_synchronized_step_mlmc, author = {Muchandimath, Sanjan C. and Gorodetsky, Alex A.}, title = {Synchronized step multilevel Markov chain Monte Carlo}, howpublished = {arXiv preprint}, year = {2025}, url = {https://arxiv.org/pdf/2501.16538}, note = {arXiv preprint} }We propose SYNCE (synchronized step correlation enhancement), a new algorithm for coupling Markov chains within multilevel Markov chain Monte Carlo (ML-MCMC) estimators. We apply this algorithm to solve Bayesian inverse problems using multiple model fidelities. SYNCE is inspired by the concept of common random number coupling in Markov chain Monte Carlo sampling. Unlike state-of-the-art methods that rely on the overlap of level-wise posteriors, our approach enables effective coupling even when posteriors differ substantially. This overlap-independence generates significantly higher correlation between samples at different fidelity levels, improving variance reduction and computational efficiency in the ML-MCMC estimator. We prove that SYNCE admits a unique invariant probability measure and demonstrate that the coupled chains converge to this measure faster than existing overlap-dependent methods, particularly when models are dissimilar. Numerical experiments validate that SYNCE consistently outperforms current coupling strategies in terms of computational efficiency and scalability across varying model fidelities and problem dimensions.
@misc{guo2025_program_synthesis_tn_search, author = {Guo, Zheng and Deshpande, Aditya S. and Kiedrowski, Brian C. and Wang, Xinyu and Gorodetsky, Alex A.}, title = {Tensor network structure search using program synthesis}, howpublished = {arXiv preprint}, year = {2025}, url = {https://arxiv.org/pdf/2502.02711}, note = {arXiv preprint} }Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network structure search a difficult problem. Existing solutions typically rely on sampling and compressing numerous candidate structures; these procedures are computationally expensive and therefore limiting for practical applications. We address this challenge by viewing tensor network structure search as a program synthesis problem and introducing an efficient constraint-based assessment method that avoids costly tensor decomposition. Specifically, we establish a correspondence between transformation programs and network structures. We also design a novel operation named output-directed splits to reduce the search space without hindering expressiveness. We then propose a synthesis algorithm to identify promising network candidates through constraint solving, and avoid tensor decomposition for all but the most promising candidates. Experimental results show that our approach improves search speed by up to $10\times$ and achieves compression ratios $1.5\times$ to $3\times$ better than state-of-the-art. Notably, our approach scales to larger tensors that are unattainable by prior work. Furthermore, the discovered topologies generalize well to similar data, yielding compression ratios up to $2.4\times$ better than a generic structure while the runtime remains around $110$ seconds.
@misc{mustaev2024_switching_kalman_filter_sensor_corruption, author = {Mustaev, Artem and Galioto, Nicholas and Boler, Matt and Jakeman, John D. and Safta, Cosmin and Gorodetsky, Alex A.}, title = {A switching Kalman filter approach to online mitigation and correction sensor corruption for inertial navigation}, howpublished = {arXiv preprint}, year = {2024}, url = {https://arxiv.org/pdf/2412.06601}, note = {arXiv preprint} }This paper introduces a novel approach to detect and address faulty or corrupted external sensors in the context of inertial navigation by leveraging a switching Kalman Filter combined with parameter augmentation. Instead of discarding the corrupted data, the proposed method retains and processes it, running multiple observation models simultaneously and evaluating their likelihoods to accurately identify the true state of the system. We demonstrate the effectiveness of this approach to both identify the moment that a sensor becomes faulty and to correct for the resulting sensor behavior to maintain accurate estimates. We demonstrate our approach on an application of balloon navigation in the atmosphere and shuttle reentry. The results show that our method can accurately recover the true system state even in the presence of significant sensor bias, thereby improving the robustness and reliability of state estimation systems under challenging conditions. We also provide a statistical analysis of problem settings to determine when and where our method is most accurate and where it fails.
@misc{gorodetsky2024_grouped_acv, author = {Gorodetsky, Alex A. and Jakeman, John D. and Eldred, Michael S.}, title = {Grouped approximate control variate estimators}, howpublished = {arXiv preprint}, year = {2024}, url = {https://arxiv.org/pdf/2402.14736}, note = {arXiv preprint} }This paper analyzes the approximate control variate (ACV) approach to multifidelity uncertainty quantification in the case where weighted estimators are combined to form the components of the ACV. The weighted estimators enable one to precisely group models that share input samples to achieve improved variance reduction. We demonstrate that this viewpoint yields a generalized linear estimator that can assign any weight to any sample. This generalization shows that other linear estimators in the literature, particularly the multilevel best linear unbiased estimator (ML-BLUE) of Schaden and Ullman in 2020, becomes a specific version of the ACV estimator of Gorodetsky, Geraci, Jakeman, and Eldred, 2020. Moreover, this connection enables numerous extensions and insights. For example, we empirically show that having non-independent groups can yield better variance reduction compared to the independent groups used by ML-BLUE. Furthermore, we show that such grouped estimators can use arbitrary weighted estimators, not just the simple Monte Carlo estimators used in ML-BLUE. Furthermore, the analysis enables the derivation of ML-BLUE directly from a variance reduction perspective, rather than a regression perspective.
@misc{de2020_breaking_posterior_symmetries, author = {De, Saibal and Salehi, Hadi and Gorodetsky, Alex A.}, title = {Efficient MCMC sampling for Bayesian matrix factorization by breaking posterior symmetries}, howpublished = {arXiv preprint}, year = {2020}, url = {https://arxiv.org/abs/2006.04295}, note = {arXiv preprint} }Bayesian low-rank matrix factorization techniques have become an essential tool for relational data analysis and matrix completion. A standard approach is to assign zero-mean Gaussian priors on the columns or rows of factor matrices to create a conjugate system. This choice of prior leads to simple implementations; however it also causes symmetries in the posterior distribution that can severely reduce the efficiency of Markov-chain Monte-Carlo (MCMC) sampling approaches. In this paper, we propose a simple modification to the prior choice that provably breaks these symmetries and maintains/improves accuracy. Specifically, we provide conditions that the Gaussian prior mean and covariance must satisfy so the posterior does not exhibit invariances that yield sampling difficulties. For example, we show that using non-zero linearly independent prior means significantly lowers the autocorrelation of MCMC samples, and can also lead to lower reconstruction errors.
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