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：物理知情神经网络(PINNs)是寻找解决方案和确定部分差异方程参数的灵活办法,大多数关于这一专题的工作都假定无噪音数据或受弱高西亚噪音污染的数据。我们表明标准PINN框架在非加西噪音情况下崩溃。我们给解决这一根本问题提供了办法,我们提议联合培训一种能源模型,以了解正确的噪音分布。我们用多个例子来说明我们方法的改进表现。