ST-PINN: A Self-Training Physics-Informed Neural Network for Partial Differential Equations

TL;DR

ST-PINN introduces a self-training mechanism into physics-informed neural networks, using pseudo labels to enhance learning of physical laws, leading to improved accuracy and convergence in solving PDEs across various applications.

Contribution

This is the first integration of self-training into physics-informed neural networks, significantly improving their accuracy and convergence for PDE solving.

Findings

Outperforms existing PINNs by 1.33x-2.54x in accuracy.

Enhances physical information learning and convergence.

Validated on five diverse PDE problems.

Abstract

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast PDE solving in various applications. To address the issue of low accuracy and convergence problems of existing PINNs, we propose a self-training physics-informed neural network, ST-PINN. Specifically, ST-PINN introduces a pseudo label based self-learning algorithm during training. It employs governing equation as the pseudo-labeled evaluation index and selects the highest confidence examples from the sample points to attach the pseudo labels. To our best knowledge, we are the first to incorporate a self-training mechanism into physics-informed learning. We conduct experiments on five PDE problems in different fields and scenarios. The results demonstrate that the proposed method allows the network to learn more physical information and benefit convergence. The ST-PINN outperforms existing physics-informed neural network methods and improves the accuracy by a factor of 1.33x-2.54x. The code of ST-PINN is available at GitHub: https://github.com/junjun-yan/ST-PINN.