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）为偏微分方程的求解与参数辨识提供了一种灵活的方法。现有研究大多假设数据无噪声或仅受弱高斯噪声污染。本文证明，在非高斯噪声存在时，标准PINN框架将失效。我们提出了一种解决该根本问题的方法，建议通过联合训练能量基模型（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在性能上的改进。