Adversarial Learning for Neural PDE Solvers with Sparse Data
This addresses the challenge of training neural PDE solvers with sparse data, which is incremental as it builds on existing methods by focusing on model weaknesses.
The study tackled the problem of data scarcity and robustness in neural PDE solvers by introducing SMART, a universal learning strategy that reduces generalization error, leading to significant improvements in prediction accuracy across various PDE scenarios.
Neural network solvers for partial differential equations (PDEs) have made significant progress, yet they continue to face challenges related to data scarcity and model robustness. Traditional data augmentation methods, which leverage symmetry or invariance, impose strong assumptions on physical systems that often do not hold in dynamic and complex real-world applications. To address this research gap, this study introduces a universal learning strategy for neural network PDEs, named Systematic Model Augmentation for Robust Training (SMART). By focusing on challenging and improving the model's weaknesses, SMART reduces generalization error during training under data-scarce conditions, leading to significant improvements in prediction accuracy across various PDE scenarios. The effectiveness of the proposed method is demonstrated through both theoretical analysis and extensive experimentation. The code will be available.