Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak Gaussian noise. We show that the standard PINN framework breaks down in case of non-Gaussian noise. We give a way of resolving this fundamental issue and we propose to jointly train an energy-based model (EBM) to learn the correct noise distribution. We illustrate the improved performance of our approach using multiple examples.

翻译：物理信息神经网络（PINNs）为求解偏微分方程和识别其参数提供了一种灵活方法。现有研究多假设数据无噪声或仅受弱高斯噪声干扰。本文证明标准PINN框架在非高斯噪声下会失效，并提出解决这一根本性问题的方案：通过联合训练能量基模型（EBM）来学习正确的噪声分布。我们通过多个算例展示了该方法性能的提升。