An acceleration strategy for randomize-then-optimize sampling via deep neural networks

TL;DR

This paper introduces a deep neural network surrogate to accelerate randomize-then-optimize sampling in Bayesian inverse problems, significantly reducing computational costs while maintaining accuracy.

Contribution

The authors develop a goal-oriented DNN surrogate for RTO, enabling faster sampling by approximating the forward model locally around the posterior.

Findings

DNN-RTO outperforms traditional RTO in computational efficiency.

The method maintains high accuracy in Bayesian inverse problems.

Significant reduction in evaluation time for complex models.

Abstract

Randomize-then-optimize (RTO) is widely used for sampling from posterior distributions in Bayesian inverse problems. However, RTO may be computationally intensive for complexity problems due to repetitive evaluations of the expensive forward model and its gradient. In this work, we present a novel strategy to substantially reduce the computation burden of RTO by using a goal-oriented deep neural networks (DNN) surrogate approach. In particular, the training points for the DNN-surrogate are drawn from a local approximated posterior distribution, and it is shown that the resulting algorithm can provide a flexible and efficient sampling algorithm, which converges to the direct RTO approach. We present a Bayesian inverse problem governed by a benchmark elliptic PDE to demonstrate the computational accuracy and efficiency of our new algorithm (i.e., DNN-RTO). It is shown that with our algorithm, one can significantly outperform the traditional RTO.