Hyper-differential sensitivity analysis with respect to model discrepancy: Optimal solution updating

A common goal throughout science and engineering is to solve optimization problems constrained by computational models. However, in many cases a high-fidelity numerical emulation of systems cannot be optimized due code complexity costs which prohibit the use intrusive query algorithms. Rather, lower-fidelity models are constructed enable algorithms for large-scale optimization. As result discrepancy between high low-fidelity models, optimal solutions determined using frequently far from true optimality. In this article we introduce novel approach that uses post-optimality sensitivities with respect model update solution. Limited data used calibrate Bayesian framework turn propagated through problem. Our formulation exploits structure sensitivity operator achieve scalability. Numerical results demonstrate how an solution computed may significantly improved limited evaluations model.