Auxiliary-Tasks Learning for Physics-Informed Neural Network-Based Partial Differential Equations Solving

TL;DR

This paper introduces auxiliary-task learning modes into physics-informed neural networks (PINNs) to significantly improve their accuracy and convergence in solving partial differential equations, marking a novel approach in physics-informed learning.

Contribution

The study pioneers the integration of auxiliary-task learning modes in PINNs and employs gradient cosine similarity to enhance PDE solving performance.

Findings

Auxiliary-task learning modes significantly improve PINN accuracy.

Maximum performance boost of 96.62% over original PINNs.

Experiments on three PDE problems demonstrate effectiveness.

Abstract

Physics-informed neural networks (PINNs) have emerged as promising surrogate modes for solving partial differential equations (PDEs). Their effectiveness lies in the ability to capture solution-related features through neural networks. However, original PINNs often suffer from bottlenecks, such as low accuracy and non-convergence, limiting their applicability in complex physical contexts. To alleviate these issues, we proposed auxiliary-task learning-based physics-informed neural networks (ATL-PINNs), which provide four different auxiliary-task learning modes and investigate their performance compared with original PINNs. We also employ the gradient cosine similarity algorithm to integrate auxiliary problem loss with the primary problem loss in ATL-PINNs, which aims to enhance the effectiveness of the auxiliary-task learning modes. To the best of our knowledge, this is the first study to introduce auxiliary-task learning modes in the context of physics-informed learning. We conduct experiments on three PDE problems across different fields and scenarios. Our findings demonstrate that the proposed auxiliary-task learning modes can significantly improve solution accuracy, achieving a maximum performance boost of 96.62% (averaging 28.23%) compared to the original single-task PINNs. The code and dataset are open source at https://github.com/junjun-yan/ATL-PINN.