Hyper-differential sensitivity analysis with respect to model discrepancy: Sequential optimal experimental design
This addresses optimization challenges in the physical sciences where computational costs are high, but it is incremental as it builds on existing sensitivity analysis methods.
The paper tackles the problem of suboptimal solutions in large-scale optimization due to discrepancies between high- and low-fidelity models, by proposing a framework that uses limited high-fidelity simulations to update solutions, resulting in significant improvements with only a few evaluations.
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.