More Consistent Accuracy PINN via Alternating Easy-Hard Training

2025-12-19

AI Summary

To address the training instability, large accuracy fluctuations, and poor generalization across diverse problems inherent in Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs), this work proposes an Alternating Easy–Hard Sample Prioritization Training strategy. The method jointly couples hard-first prioritization—driven by residuals and gradients—with easy-first prioritization—guided by low-frequency components and initial/boundary conditions. We introduce, for the first time, an alternating optimization framework integrating residual-weighted sampling, frequency-domain analysis, and dynamic loss reweighting, augmented with automatic differentiation and adaptive mesh redistribution. This approach overcomes the limitations of single-priority strategies, achieving relative L² errors of 1e−5–1e−6 on PDEs with steep gradients, strong nonlinearity, and high dimensionality. It consistently outperforms state-of-the-art baselines by 3–10× in accuracy, while significantly enhancing robustness and generalization consistency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning with Manifolds
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Address inconsistent PINN performance across different PDE types
• Combine hard and easy prioritization strategies for hybrid training
• Improve accuracy and reliability on PDEs with challenging characteristics

Innovation

• Alternating easy-hard training algorithm for PINNs
• Hybrid strategy combining hard and easy prioritization
• Achieves consistent high accuracy across diverse PDEs