Efficient derivative-free Bayesian inference for large-scale inverse problems

Abstract We consider Bayesian inference for large-scale inverse problems, where computational challenges arise from the need repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible, since they typically require O ( 1 0 4 stretchy="false">) model runs, or more. Moreover, is often given as a black box impractical to differentiate. Therefore derivative-free algorithms are highly desirable. propose framework, which built on Kalman methodology, efficiently perform in such problems. The basic method based approximation filtering distribution novel mean-field dynamical system, into problem embedded observation operator. Theoretical properties established linear demonstrating that desired posterior by steady state law and proving exponential convergence it. suggests that, nonlinear problems close Gaussian, sequentially computing this provides basis efficient iterative methods approximate posterior. Ensemble applied obtain interacting particle system approximations model; practical strategies further reduce memory cost methodology presented, including low-rank bi-fidelity approach. effectiveness framework demonstrated several numerical experiments, proof-of-concept linear/nonlinear examples two applications: learning permeability parameters subsurface flow; subgrid-scale global climate stochastic ensemble filter various square-root filters all employed compared numerically. results demonstrate proposed method, competitive with pre-existing Kalman-based