Physics-informed Neural Networks with Unknown Measurement Noise
This addresses a fundamental issue in PINNs for solving partial differential equations with unknown noise, though it appears incremental as it builds on the standard PINN framework.
The paper tackled the breakdown of physics-informed neural networks (PINNs) under non-Gaussian noise by proposing a method to jointly train an energy-based model to learn the noise distribution, resulting in improved performance demonstrated through multiple examples.
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.