Physics-Informed Neural Networks (PINNs) are a class of deep learning models designed to solve partial differential equations by incorporating physical laws directly into the loss function. However, the internal covariate shift, which has been largely overlooked, hinders the effective utilization of neural network capacity in PINNs. To this end, we propose Mask-PINNs, a novel architecture designed to address this issue in PINNs. Unlike traditional normalization methods such as BatchNorm or LayerNorm, we introduce a learnable, nonlinear mask function that constrains the feature distributions without violating underlying physics. The experimental results show that the proposed method significantly improves feature distribution stability, accuracy, and robustness across various activation functions and PDE benchmarks. Furthermore, it enables the stable and efficient training of wider networks a capability that has been largely overlooked in PINNs.
View on arXiv@article{jiang2025_2505.06331,
title={ Mask-PINNs: Regulating Feature Distributions in Physics-Informed Neural Networks },
author={ Feilong Jiang and Xiaonan Hou and Jianqiao Ye and Min Xia },
journal={arXiv preprint arXiv:2505.06331},
year={ 2025 }
}