Physics-informed Neural Networks with Unknown Measurement Noise

Philipp Pilar; Niklas Wahlström

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arXiv · 2211.15498

Physics-informed Neural Networks with Unknown Measurement Noise

Philipp Pilar·Niklas Wahlström

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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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Philipp Pilar, Niklas Wahlström. 2022-11-28. Physics-informed Neural Networks with Unknown Measurement Noise. https://arxiv.org/abs/2211.15498

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