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Poster
in
Workshop: AI4DifferentialEquations In Science

Heteroscedastic uncertainty quantification in Physics-Informed Neural Networks

Olivier Claessen · Yuliya Shapovalova · Tom Heskes


Abstract:

Physics-informed neural networks (PINNs) provide a machine learning framework to solve differential equations. However, PINNs do not inherently consider measurement noise or model uncertainty. In this paper, we propose the UQ-PINN which is an extension of the PINN with additional outputs to approximate the additive noise. The multi-output architecture enables approximation the mean and standard deviation over data using negative Gaussian log-likelihood loss. The performance of the UQ-PINN is demonstrated on the Poisson equation with additive noise.

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