Physics-informed neural networks via stochastic Hamiltonian dynamics learning

In this paper, we propose novel learning frameworks to tackle optimal control problems by applying the Pontryagin maximum principle and then solving for a Hamiltonian dynamical system. Applying the Pontryagin maximum principle to the original optimal control problem shifts the learning focus to redu...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Bajaj, Chandrajit, Nguyen, Minh
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 26.04.2024
Subjects:	Learning Maximum principle Optimal control Robustness Stochastic models
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	In this paper, we propose novel learning frameworks to tackle optimal control problems by applying the Pontryagin maximum principle and then solving for a Hamiltonian dynamical system. Applying the Pontryagin maximum principle to the original optimal control problem shifts the learning focus to reduced Hamiltonian dynamics and corresponding adjoint variables. Then, the reduced Hamiltonian networks can be learned by going backwards in time and then minimizing loss function deduced from the Pontryagin maximum principle's conditions. The learning process is further improved by progressively learning a posterior distribution of the reduced Hamiltonians. This is achieved through utilizing a variational autoencoder which leads to more effective path exploration process. We apply our learning frameworks called NeuralPMP to various control tasks and obtain competitive results.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2111.08108