Bayesian learning of dynamical systems under uncertainty

Abstract: We analyze a Bayesian probabilistic formulation for system identification of dynamical systems. The approach uses an approximate marginal Markov Chain Monte Carlo algorithm to directly discover a system from data. The posterior distribution simultaneously accounts for unknown parameters, model form uncertainty, and measurement noise. As a result of this feature, we show that our approach becomes more robust than current state-of-the-art methods that rely on more commonly used optimization objectives such as sparse identification of nonlinear dynamics (SINDy), dynamic mode decomposition (DMD), universal differential equations, etc. The framework also generalizes common variants of approaches based on Markov parameter estimation in linear system ID and multiple shooting in nonlinear settings. The approach is approximation-format agnostic and works with both linear and nonlinear dynamical system parameterizations. In this talk, we discuss why this approach results in more robust identification than a variant of linear system identification and its connection to the multiple shooting methods that are commonly used in nonlinear problems. We show examples demonstrating that we outperform more standard operator inference and vector-field inference approaches when data becomes sparse and noisy. We then focus our discussions on how physical knowledge can be embedded into these approaches, and focus on extending it to direct identification of system Hamiltonians. Here, our approach improves upon existing approaches by encoding the fact that the data generating process is symplectic directly into our learning objective. 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 several Hamiltonian benchmarking systems. Time permitting, we discuss more recent work that aims to develop an online system identification variant of this work through variational inference.

Bio: Alex Gorodetsky is an Assistant Professor of Aerospace Engineering at the University of Michigan. His research interests include using applied mathematics and computational science to develop algorithms to enhance autonomous decision-making under uncertainty. Toward this goal, he pursues research in wide-ranging areas including uncertainty quantification, statistical inference, control, and optimization. Prior to coming to the University of Michigan, Alex was the John von Neumann Postdoctoral Research Fellow at Sandia National Laboratories in Albuquerque, New Mexico. At Sandia, Alex worked in the Optimization and Uncertainty Quantification Group on algorithms for propagating uncertainty through physical systems described with computationally expensive simulations. Alex won the Air Force Young Investigator Award in 2018 and the NSF CAREER Award in 2023.

*** The event will take place in a hybrid format. The location for in-person attendance will be room 1303 EECS. Attendance will also be available via Zoom.

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Zoom Passcode information is also available upon request to Sher Nickrand ([email protected])

*** This seminar was not recorded per request by Professor Gorodetsky***