Efficient geometric Markov chain Monte Carlo for nonlinear Bayesian inversion enabled by derivative-informed neural operators

arXiv:2403.08220v1 Announce Type: cross
Abstract: We propose an operator learning approach to accelerate geometric Markov chain Monte Carlo (MCMC) for solving infinite-dimensional nonlinear Bayesian inverse problems. While geometric MCMC employs high-quality proposals that adapt to posterior local geometry, it requires computing local gradient and Hessian information of the log-likelihood, incurring a high cost when the parameter-to-observable (PtO) map is defined through expensive model simulations. We consider a delayed-acceptance geometric MCMC method driven by a neural operator surrogate of the PtO …

abstract adapt arxiv bayesian computing cs.lg cs.na geometry gradient markov math.na mcmc operators posterior proposals quality stat.co stat.ml type