Physics-informed Neural Networks with Unknown Measurement Noise

TL;DR

The paper addresses the vulnerability of physics-informed neural networks (PINNs) to non-Gaussian measurement noise and proposes jointly training an energy-based model (EBM) to learn the true noise distribution. By integrating the learned noise model with PINN training, the approach captures complex noise profiles and improves PDE solution accuracy and parameter identification under non-Gaussian conditions. Demonstrations across multiple examples show enhanced robustness and performance when noise deviates from Gaussian assumptions. This work broadens the applicability of PINNs to real-world noisy data, enabling more reliable PDE discovery and parameter inference in practical settings.

Abstract

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.

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• Figure 1: Sample figure caption.