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)是一种灵活的方法，可用于求解偏微分方程并识别其参数。该领域的大多数研究假设数据无噪声，或数据受弱高斯噪声污染。我们发现，标准PINN框架在非高斯噪声情况下会失效。我们提出了一种解决这一根本问题的方法，建议联合训练一个基于能量的模型(EBM)以学习正确的噪声分布。通过多个示例，我们展示了该方法在性能上的改进。