Physics-Informed Neural Optimality

Oct 27, 2023
In continuous environments, optimality-related quantities for finite-dimensional dynamical systems usually exist in the lifted function/functional spaces, which are solutions to optimality-induced partial differential equations (PDEs). We develop analysis and computation tools in this regard.

Posts

Chairing the Invited Session on AI-Enhanced Safety-Certifiable Autonomous Vehicles at IEEE ITSC 2024.
The invited session AI-Enhanced Safety-Certifiable Autonomous Vehicles was successfully held at the 27th IEEE International Conference on Intelligent Transportation Systems (ITSC).
Sep 25, 2024 1 min read
Project
Two works were presented in July.
Two conferences, ACC and ICML, were held in July. The workw on a recently developed Zubov-Koopman operator for constructing Lyapunov functions and a PINN method for designing an optimal stabilizing controller were presented.
Jul 30, 2024 1 min read
Project
Talk on Physics-Informed Stability Control for Nonlinear Systems at CAIMS 2024, Kingston, Ontario, Canada.
A talk on Physics-Informed Characterization and Control of Stability for Nonlinear Systems was presented at the CAIMS 2024 meeting in the subsession Recent Progress on the Intersections of Nonlinear Dynamics, Control, Learning, and Optimization.
Jun 27, 2024 2 min read
Project
A novel tool for learning and verifying neural Lyapunov functions and regions of attraction was presented.
The tool paper TOOL LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of Attraction was presented at the 27th ACM International Conference on Hybrid Systems: Computation and Control (HSCC) in Hong Kong and gained significant attention. What distinguishes the tool from others in the literature is its ability to provide verified regions of attraction close to the domain of attraction.
May 16, 2024 1 min read
Project
A novel tool for learning and verifying neural Lyapunov functions and regions of attraction was presented.
One ICML 2024 Paper Accepted
Our paper, Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification has been accepted to the 2024 International Conference on Machine Learning (ICML24), Vienna.
May 1, 2024 1 min read
Project
One ICML 2024 Paper Accepted
One ADHS 2024 Paper Accepted
Our paper, LyZNet with Control: Physics-Informed Neural Network Control of Nonlinear Systems with Formal Guarantees has been accepted to the 8th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS), Boulder.
Mar 15, 2024 1 min read
Project
Multiple Conference Papers Accepted
Two papers have been accepted to the 2024 American Control Conference (ACC) in Toronto, and one tool paper has been accepted to the 2024 ACM International Conference on Hybrid Systems: Computation and Control (HSCC) in Hong Kong.
Jan 22, 2024 1 min read
Project Project

Publications

Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification
Y. Meng, R. Zhou, A. Mukherjee, M. Fitzsimmons, C. Song, J. Liu
PDF Cite Project Poster
Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification
Compositionally Verifiable Vector Neural Lyapunov Functions for Stability Analysis of Interconnected Nonlinear Systems
J. Liu, Y. Meng, M. Fitzsimmons, R. Zhou
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Physics-Informed Extreme Learning Machine Lyapunov Functions
R.Zhou, M. Fitzsimmons, Y. Meng, J. Liu
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Physics-Informed Extreme Learning Machine Lyapunov Functions
LyZNet with Control: Physics-Informed Neural Network Control of Nonlinear Systems with Formal Guarantees
J. Liu, Y. Meng, R. Zhou
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LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of Attraction
J. Liu, Y. Meng, M. Fitzsimmons, R. Zhou
PDF Cite Project Poster DOI
LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of Attraction
Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verification
J. Liu, Y. Meng, M. Fitzsimmons, R. Zhou
PDF Project Source Document
Towards Learning and Verifying Maximal Neural Lyapunov Functions
J. Liu, Y. Meng, M. Fitzsimmons, R. Zhou
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