Bayesian Reasoning for Physics Informed Neural Networks

arXiv:2308.13222v2 Announce Type: replace-cross
Abstract: We present the application of the physics-informed neural network (PINN) approach in Bayesian formulation. We have adopted the Bayesian neural network framework to obtain posterior densities from Laplace approximation. For each model or fit, the evidence is computed, which is a measure that classifies the hypothesis. The optimal solution is the one with the highest value of evidence. We have proposed a modification of the Bayesian algorithm to obtain hyperparameters of the model. We have …

abstract application approximation arxiv bayesian cs.lg evidence framework hypothesis laplace approximation network networks neural network neural networks physics physics.comp-ph physics.flu-dyn physics-informed pinn posterior reasoning stat.ml type