Two-Step Bayesian PINNs for Uncertainty Estimation

Pablo Flores, Olga Graf, Pavlos Protopapas, Karim Pichara

Keywords: Physics Informed Neural Networks, Uncertainty Quantification, Differential Equations, Cosmology, Fermentation, Inverse Problem

TL;DR: We use a two-step procedure for training Bayesian NNs to obtain uncertainties over DE solutions. We use PINNs' error bounds to improve uncertainty quality. The uncertainties are used to solve inverse problems in cosmology and fermentation systems.

Abstract: We use a two-step procedure to train Bayesian neural networks that provide uncertainties over the solutions to differential equation (DE) systems provided by Physics-Informed Neural Networks (PINNs). We take advantage of available error bounds over PINNs to formulate a heteroscedastic variance that improves the uncertainty estimation. Furthermore, we solve forward problems and utilize the uncertainties obtained to improve parameter estimation in inverse problems in the fields of cosmology and fermentation.

Submission Number: 21