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Neural networks are universal approximators, yet learned models rarely come with rigorous guarantees. Typical statistical learning bounds are often too conservative, and probabilistic guarantees do not certify the correctness of a specific computed solution. 更多阅读

In this talk, we connect physics-informed learning with computer-assisted proofs to turn neural models into certifiable computational tools. The central idea is to train neural networks using equations that encode system dynamics and desired properties, then formally verify that the learned functions satisfy the required conditions. 更多阅读

More specifically, we study partial differential equation characterizations arising in stability analysis and optimal control of nonlinear dynamical systems. We use physics-informed neural networks to learn Lyapunov and value functions, formally verify regions of attraction and stabilizing controllers, and derive certified a posteriori error bounds. We also discuss learning unknown dynamics through Koopman generators and recent results on neural Lyapunov functions for homogeneous systems, including a surprising counterexample discovered by AI that disproves an open conjecture.

Bio: Jun Liu is a Professor of Applied Mathematics and Canada Research Chair at the University of Waterloo, where he directs the Hybrid Systems Laboratory and serves as Associate Director of the Waterloo Data and Artificial Intelligence Institute. He received a B.S. in Mathematics and Applied Mathematics from Shanghai Jiao Tong University in 2002, an M.S. in Mathematics from Peking University in 2005, and a Ph.D. in Applied Mathematics from the University of Waterloo in 2011. He held an NSERC Postdoctoral Fellowship at Caltech and was a Lecturer in Systems and Control Engineering at the University of Sheffield before joining the University of Waterloo. His research interests include hybrid systems and control, formal methods, optimization and learning, and robotics.