Adaptive Physics-Informed Neural Networks for Markov-Chain Monte Carlo [article]

Mohammad Amin Nabian, Hadi Meidani
2020 arXiv   pre-print
In this paper, we propose the Adaptive Physics-Informed Neural Networks (APINNs) for accurate and efficient simulation-free Bayesian parameter estimation via Markov-Chain Monte Carlo (MCMC). We specifically focus on a class of parameter estimation problems for which computing the likelihood function requires solving a PDE. The proposed method consists of: (1) constructing an offline PINN-UQ model as an approximation to the forward model; and (2) refining this approximate model on the fly using
more » ... amples generated from the MCMC sampler. The proposed APINN method constantly refines this approximate model on the fly and guarantees that the approximation error is always less than a user-defined residual error threshold. We numerically demonstrate the performance of the proposed APINN method in solving a parameter estimation problem for a system governed by the Poisson equation.
arXiv:2008.01604v1 fatcat:igpieoqkr5avjje32xishbvq5u