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 by 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辨识其参数提供了一种灵活的方法。该领域的大多数研究假设数据无噪声，或仅受弱高斯噪声污染。我们证明，在非高斯噪声情况下，标准PINN框架会失效。我们提出解决这一根本问题的方法，并建议联合训练一个基于能量的模型（EBM）来学习正确的噪声分布。通过多个示例，我们展示了所提方法性能的提升。