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

• Published in: Chinese Control Conference pp. 8759 - 8764
• Main Authors: Cao, Yuandong, So, Chi Chiu, Wang, Junmin, Yung, Siu Pang
• Format: Conference Proceeding
• Language: English
• Published: Technical Committee on Control Theory, Chinese Association of Automation 28.07.2024
• Subjects: Adaptive systems; Decentralized control; Deep learning; Inverse problems; Neural networks; Numerical simulation; Optimal control; Partial differential equations; Physics-Informed neural network
• ISSN: 1934-1768
• DOI: 10.23919/CCC63176.2024.10662626

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.