  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.
