Data-driven optimal control with neural network modeling of gradient flows

Thumbnail Image
Date
2023-12-02
Authors
Tian, Xuping
Lui, Hailiang
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
arXiv
Research Projects
Organizational Units
Organizational Unit
Organizational Unit
Journal Issue
Is Version Of
Versions
Series
Department
Mechanical EngineeringMathematics
Abstract
Extracting physical laws from observation data is a central challenge in many diverse areas of science and engineering. We propose Optimal Control Neural Networks (OCN) to learn the laws of vector fields in dynamical systems, with no assumption on their analytical form, given data consisting of sampled trajectories. The OCN framework consists of a neural network representation and an optimal control formulation. We provide error bounds for both the solution and the vector field. The bounds are shown to depend on both the training error and the time step between the observation data. We also demonstrate the effectiveness of OCN, as well as its generalization ability, by testing on several canonical systems, including the chaotic Lorenz system.
Comments
This is a preprint from Tian, Xuping, Baskar Ganapathysubramanian, and Hailiang Liu. "Data-driven optimal control with neural network modeling of gradient flows." arXiv preprint arXiv:2312.01165 (2023). doi: https://doi.org/10.48550/arXiv.2312.01165. Copyright 2023, The Authors. CC-BY.
Description
Keywords
Citation
DOI
Subject Categories
Copyright
Collections