System Stabilization of PDEs using Physics-Informed Neural Networks (PINNs)

Yuandong Cao*, Chi Chiu So, Junmin Wang, Siu Pang Yung

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

As a popular neural network model for solving forward and inverse problems in partial differential equation (PDE) control, Physics-Informed Neural Networks (PINNs) have received extensive attention in recent years and have made break-throughs in various fields. With the application of PINNs being extended to optimal control problems constrained by PDEs, where the control PDE is fully known, the problem objective is to find a control variable to minimize the desired cost objective. In this paper, with the idea of using PINNs to solve optimal control problems, we investigated effective methods to find boundary control and distributed control which can drive the PDE state towards unstable zero-point solutions. We also demonstrated the effectiveness of boundary control and distributed control through numerous numerical experiments on Reaction-Diffusion equations and Burgers' equations.

Original languageEnglish
Title of host publicationProceedings of the 43rd Chinese Control Conference, CCC 2024
EditorsJing Na, Jian Sun
PublisherIEEE Computer Society
Pages8759-8764
Number of pages6
ISBN (Electronic)9789887581581
DOIs
Publication statusPublished - 2024
Event43rd Chinese Control Conference, CCC 2024 - Kunming, China
Duration: 28 Jul 202431 Jul 2024

Publication series

NameChinese Control Conference, CCC
ISSN (Print)1934-1768
ISSN (Electronic)2161-2927

Conference

Conference43rd Chinese Control Conference, CCC 2024
Country/TerritoryChina
CityKunming
Period28/07/2431/07/24

Keywords

  • Deep learning
  • Optimal control
  • Physics-Informed neural network

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