More Consistent Accuracy PINN via Alternating Easy-Hard Training

TL;DR

This paper introduces an alternating training strategy for PINNs that combines easy and hard prioritization methods, resulting in more accurate and reliable solutions for complex PDEs across various problem types.

Contribution

The paper proposes a novel hybrid alternating training algorithm for PINNs that improves accuracy and robustness across diverse PDE problems by leveraging the strengths of both prioritization approaches.

Findings

Achieves relative L2 errors of O(10^-5) to O(10^-6) on challenging PDEs

Provides more consistent accuracy across different PDE types

Outperforms baseline methods in terms of reliability and robustness

Abstract

Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by finite element methods are widely adopted, recent research suggests that easy prioritization can also be effective. Nevertheless, we find that both approaches exhibit notable trade-offs and inconsistent performance across PDE types. To address this issue, we develop a hybrid strategy that combines the strengths of hard and easy prioritization through an alternating training algorithm. On PDEs with steep gradients, nonlinearity, and high dimensionality, the proposed method achieves consistently high accuracy, with relative L2 errors mostly in the range of O(10^-5) to O(10^-6), significantly surpassing baseline methods. Moreover, it offers greater reliability across diverse problems, whereas compared approaches often suffer from variable accuracy depending on the PDE. This work provides new insights into designing hybrid training strategies to enhance the performance and robustness of PINNs.