Physics-informed neural network uncertainty assessment through Bayesian inference.

Abstract

This work presents a Bayesian approach to evaluating the uncertainty of physics-informed neural network models. The proposed strategy uses a hybrid methodology for training and assessing the uncertainty of model parameters. In the first part of the training, a gradient-based algorithm is used to train and obtain the weights. In the second stage, a Markov Chain Monte Carlo algorithm is used to evaluate the uncertainty of the network weights. The developed method was used to solve Burger’s equation, and the results show that it was possible to characterize the uncertainty region of the PINNs’ prediction.