Physics-informed neural networks with unknown measurement noise
Keywords: physics-informed neural networks, energy-based models, non-Gaussian noise, system identification
TL;DR: We use energy-based models to learn the noise distribution jointly with the PINN prediction.
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 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
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Submission Number: 2522
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