Hyper-differential sensitivity analysis with respect to model discrepancy: Sequential optimal experimental design

TL;DR

This paper introduces a Bayesian sequential experimental design framework leveraging hyper-differential sensitivity analysis to efficiently improve optimization solutions by strategically using limited high-fidelity model evaluations.

Contribution

It develops a novel Bayesian approach with pseudo-time continuation for sequential data acquisition to reduce model discrepancy in large-scale optimization.

Findings

Significant improvement in optimization accuracy with few high-fidelity evaluations.

Efficient computation of higher-accuracy solutions using pseudo-time continuation.

Framework effectively guides high-fidelity evaluations to reduce uncertainty.

Abstract

Large-scale optimization problems are ubiquitous in the physical sciences; yet, high-fidelity models can often be complex and computationally prohibitive for optimization. A practical alternative is to use a low-fidelity model to facilitate optimization. However, the discrepancy between the high- and low-fidelity models can lead to suboptimal solutions. To address this, we build on recent work in Hyper-Differential Sensitivity Analysis to leverage limited high-fidelity simulations to update the optimization solution. Our contributions in this article include: (i) incorporating pseudo-time continuation techniques to efficiently compute higher-accuracy optimal solution updates, and (ii) proposing a Bayesian framework for sequential data acquisition that strategically guides high-fidelity evaluations and reduces uncertainty in the model discrepancy estimation. Numerical results demonstrate that our framework delivers significant improvements to optimization solutions with only a few high-fidelity evaluations.