Presented by CNEL
Computational NeuroEngineering Laboratory
“Kernel Operator-Theoretic Bayesian Filter for Nonlinear Dynamical Systems”
Thursday, Nov. 7 at 1:00pm
MALA 5050
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Abstract
Motivated by the surge of interest in Koopman operator theory, we propose a machine-learning alternative based on a functional Bayesian perspective for operator-theoretic modeling of unknown, data-driven, nonlinear dynamical systems. This formulation is directly done in an infinite-dimensional space of linear operators or Hilbert space with universal approximation property. The theory of reproducing kernel Hilbert space (RKHS) allows the lifting of nonlinear dynamics to a potentially infinite-dimensional space via linear embeddings, where a general nonlinear function is represented as a set of linear functions or operators in the functional space. This enables us to apply classical linear Bayesian methods such as the Kalman filter directly in the Hilbert space, yielding nonlinear solutions in the original input space. This kernel perspective on the Koopman operator offers two compelling advantages. First, the Hilbert space can be constructed deterministically, agnostic to the nonlinear dynamics. The Gaussian kernel is universal, approximating uniformly an arbitrary continuous target function over any compact domain. Second, Bayesian filter is an adaptive, linear minimum-variance algorithm, allowing the system to update the Koopman operator and continuously track the changes across an extended period of time, ideally suited for modern data-driven applications such as real-time machine learning using streaming data. This talk will explore several practical implementations. We demonstrate that this principled approach can obtain accurate results and outperform finite-dimensional Koopman decomposition.
Biography
Dr. Kan Li is a research scientist at the University of Florida. Dr. Li received his B.A.Sc. degree in electrical engineering from the University of Toronto and Ph.D. from UF. His primary research interests are in advanced signal processing and machine learning. He was awarded a Small Business Innovation Research grant from the National Science Foundation in 2016 for developing bio-inspired ultra-low-power embedded intelligent system, and the Best Paper Award in Signal Processing at the International Congress of Basic Science in 2023.