Adaptive Gaussian Process Regression for Bayesian inverse problems

TL;DR

This paper presents an adaptive Gaussian Process Regression method that efficiently constructs surrogate models for Bayesian inverse problems, reducing computational costs while maintaining posterior accuracy.

Contribution

It introduces a goal-oriented active learning strategy that adaptively selects training points based on their impact on the posterior distribution, improving efficiency.

Findings

Demonstrated reduced computational cost in test problems

Maintained high fidelity of posterior distributions

Effective adaptive sampling strategy for Bayesian inverse problems

Abstract

We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on optimizing both the positioning and simulation accuracy of training data in order to reduce the computational cost of simulating training data without compromising the fidelity of the posterior distributions of parameters. The method interleaves a goal-oriented active learning algorithm selecting evaluation points and tolerances based on the expected impact on the Kullback-Leibler divergence of surrogated and true posterior with a Markov Chain Monte Carlo sampling of the posterior. The performance benefit of the adaptive approach is demonstrated for two simple test problems.