Stein Variational Reduced Basis Bayesian Inversion

We propose and analyze a Stein variational reduced basis method (SVRB) to solve large-scale PDE-constrained Bayesian inverse problems. To address the computational challenge of drawing numerous samples requiring expensive PDE solves from posterior distribution, we integrate an adaptive goal-oriented model reduction technique with optimization-based gradient descent method. present detailed analyses for approximation errors potential its gradient, induced distribution measured by Kullback--Leibler divergence, as well samples. demonstrate accuracy efficiency SVRB, report results numerical experiments on problem governed diffusion random parameters both uniform Gaussian prior distributions. Over 100X speedups can be achieved while is preserved.