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

Autor:	Tian, Xuping, Ganapathysubramanian, Baskar, Liu, Hailiang
Rok vydání:	2023
Předmět:	Mathematics - Dynamical Systems Mathematics - Optimization and Control 93C15 49K15
Druh dokumentu:	Working Paper
Popis:	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. Comment: 28 pages, 8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.01165 Zobrazit plný text záznamu View this record from Arxiv