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 to code complexity and computational costs which prohibit the use of intrusive and many query algorithms. Rather, lower-fidelity models are constructed to enable intrusive algorithms for large-scale optimization. As a result of the discrepancy between high and low-fidelity models, optimal solutions determined using low-fidelity models are frequently far from true optimality. In this article we introduce a novel approach that uses post-optimality sensitivities with respect to model discrepancy to update the optimization solution. Limited high-fidelity data is used to calibrate the model discrepancy in a Bayesian framework which in turn is propagated through post-optimality sensitivities of the low-fidelity optimization problem. Our formulation exploits structure in the post-optimality sensitivity operator to achieve computational scalability. Numerical results demonstrate how an optimal solution computed using a low-fidelity model may be significantly improved with limited evaluations of a high-fidelity model.

翻译：科学与工程中的一个常见目标是解决由计算模型约束的优化问题。然而，在许多情况下，由于代码复杂性和计算成本阻碍了侵入式及多查询算法的使用，系统的高保真数值仿真无法被优化。相反，低保真度模型被构建以实现大规模优化的侵入式算法。由于高、低保真度模型之间存在差异，使用低保真度模型确定的最优解往往远非真正的最优解。在本文中，我们引入了一种新颖的方法，该方法利用针对模型差异的最优后敏感性来更新优化解。有限的低保真度数据在贝叶斯框架内用于校准模型差异，而该差异则通过低保真度优化问题的最优后敏感性传递。我们的公式利用了最优后敏感性算子中的结构以实现计算可扩展性。数值结果表明，使用低保真度模型计算得到的最优解可通过有限次的高保真度模型评估得到显著改善。