Bayesian inversion using adaptive Polynomial Chaos Kriging within Subset Simulation

• We propose a Bayesian inversion method combining adaptive Polynomial Chaos Kriging and Structural Reliability Method. An active-learning scheme is proposed in order to enrich the surrogate models informative zones. The illustrated on three inverse problems with different complexity dimensionality. enables efficiently sample from posteriors distributions for limited amount of model calls. In this paper, we approach (PCK) rare event estimation called Subset Simulation (SuS). It based recently introduced Updating reliability (BUS) framework that reformulate classical inference into problem. context, SuS aims at drawing samples posterior distribution as well estimating evidence, which usually computationally intractable when considering MCMC approaches. involves construction PCK provides both global local approximations likelihood function, through combination surrogates. Furthermore, an enriching throughout sampling procedure, improve its accuracy near regions. applicability efficiency are assessed several cases studies increasing complexity. Results highlight accurately approximating full calls, even case multi-modal posteriors, difficult using algorithms.