Title: Physics-Informed Neural Network Lyapunov Functions

Abstract: One of the longstanding challenges in systems and control is the effective construction of Lyapunov functions for formal system analysis and control. In this talk, we discuss a machine learning framework for learning Lyapunov certificates to address stability and safety problems in systems and control using physics-informed neural networks. Specifically, we obtain neural Lyapunov functions by solving characteristic partial differential equations (PDEs) for these problems with neural networks and derive sufficient conditions for the efficient verification of the learned certificates using satisfiability modulo theories (SMT) solvers. We address approximation error bounds, convergence guarantees of neural approximations, and the formal correctness of neural Lyapunov certificates. The framework is illustrated with examples from nonlinear systems and control, ranging from low- to high-dimensional systems, and shown to outperform traditional sum-of-squares (SOS) approaches in semidefinite programming.

Bio: Jun Liu is a Professor of Applied Mathematics and a Canada Research Chair at the University of Waterloo, where he directs the Hybrid Systems Lab. He received his B.S. in Applied Mathematics from Shanghai Jiao-Tong University, M.S. in Mathematics from Peking University, and Ph.D. in Applied Mathematics from the University of Waterloo. After a Postdoctoral Fellowship at Caltech, he was a Lecturer at the University of Sheffield before joining Waterloo in 2015. His research focuses on hybrid systems, control theory, optimization, and machine learning, with applications in robotics and cyber-physical systems. He has received a Marie-Curie Career Integration Grant, a Canada Research Chair (2017–2027), an Ontario Early Researcher Award, and the CAIMS/PIMS Early Career Award. His best paper awards include the Zhang Si-Ying Outstanding Youth Paper Award, the IFAC Nonlinear Analysis: Hybrid Systems (NAHS) Paper Prize, and the Oded Maler Prize (FORMATS Best Paper). Dr. Liu is a senior member of IEEE, a member of SIAM, and a lifetime member of CAIMS, and has served on editorial boards and program committees of several journals and conferences in control and systems theory.

标题：物理信息神经网络李雅普诺夫函数

摘要

作者简介