CAP Seminar Series
Title: Some topics at the intersection of control, dynamics, and learning from data
Speaker: Eduardo Sontag, Northeastern University
Venue: EENG 909b
Date and Time: Friday 13 Dec 2024, 14:00 - 15:00
Abstract: Data-driven modeling typically involves simplifications of systems through dimensionality reduction (less variables) or through dimensionality enlargement (more variables, but simpler, perhaps linear, dynamics). Autoencoders with narrow bottleneck layers are a typical approach to the former (allowing the discovery of dynamics taking place in a lower-dimensional manifold), and autoencoders with wide layers provide an approach to the later, with “neurons” in these layers thought of as “observables” in Koopman representations. In this talk, I’ll briefly discuss some theoretical results about each of these. (Joint work with M.D. Kvalheim on dimension reduction and with Z. Liu and N. Ozay on Koopman representations.)
Training of such autoencoders (or more general vector functions) is typically performed by gradient descent. Thus, it is natural to ask about the dynamics of such training, especially in the presence of errors in the estimation of the gradient. Inputs that represent perturbations from the true gradient arising from adversarial attacks, wrong evaluation by an oracle, early stopping of a simulation, inaccurate and very approximate digital twins, stochastic computations (algorithm “reproducibility”), or learning by sampling from limited data, can be formulated in terms of input to state stability (ISS), which quantifies the graceful degradation of performance of transient and asymptotic behavior. We present results for such disturbed gradient systems in the context of regression learning (joint work with A.C.B. de Oliveira and M. Siami) as well as in direct LQR algorithms (joint work with L. Cui and Z.P. Jiang).
Biography: Eduardo D. Sontag received his Licenciado in Mathematics at the University of Buenos Aires (1972) and a Ph.D. in Mathematics (1977) under Rudolf E. Kalman at the University of Florida. From 1977 to 2017, he was at Rutgers University, where he was a Distinguished Professor of Mathematics and a Member of the Graduate Faculty of the Departments of Computer Science and of Electrical and Computer Engineering and the Cancer Institute of NJ. He directed the undergraduate Biomathematics Interdisciplinary Major and the Center for Quantitative Biology, and was Graduate Director at the Institute for Quantitative Biomedicine. In January 2018, Dr. Sontag became a University Distinguished Professor in the Departments of Electrical and Computer Engineering and of BioEngineering at Northeastern University, where he is also affiliated with the Mathematics and the Chemical Engineering departments. Since 2006, he has been a Research Affiliate at the Laboratory for Information and Decision Systems, MIT , and since 2018 he has been a Faculty Member in the Program in Therapeutic Science at Harvard Medical School. His major current research interests lie in several areas of control and dynamical systems theory, systems molecular biology, cancer and immunology, machine learning, and computational biology. Sontag has authored over five hundred research papers and monographs and book chapters in the above areas with over 60,000 citations and an h-index of 106 (57 since 2019). He is a Fellow of various professional societies: IEEE , AMS, SIAM , and IFAC , and is also a member of SMB and BMES . He was awarded the Reid Prize in Mathematics in 2001, the 2002 Hendrik W. Bode Lecture Prize and the 2011 Control Systems Field Award from the IEEE , the 2022 Richard E. Bellman Control Heritage Award, the 2023 IFAC Triennial Award on Nonlinear Control, the 2002 Board of Trustees Award for Excellence in Research from Rutgers, and the 2005 Teacher/Scholar Award from Rutgers. In 2024, he was elected to the American Academy of Arts and Sciences.
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