This work introduces meta estimators that combine multiple multifidelity techniques based on control variates, importance sampling, and information reuse to yield a quasi-multiplicative amount of variance reduction. The proposed meta estimators are particularly efficient within outer-loop applications when the input distribution of the uncertainties changes during the outer loop, which is often the case in reliability-based design and shape optimization. We derive asymptotic bounds of the variance reduction of the meta estimators in the limit of convergence of the outer-loop results. We demonstrate the meta estimators, using data-driven surrogate models and biasing densities, on a design problem under uncertainty motivated by magnetic confinement fusion, namely the optimization of stellarator coil designs to maximize the estimated confinement of energetic particles. The meta estimators outperform all of their constituent variance reduction techniques alone, ultimately yielding two orders of magnitude speedup compared to standard Monte Carlo estimation at the same computational budget.
翻译:这项工作引入了基于控制变异、重要取样和信息再利用的多种多异性技术相结合的元估计值,以产生半重复性差异减少量。当外环期间不确定性变化的输入分布时,拟议的元估计值在外环应用中特别高效,这是基于可靠性的设计和形状优化中经常出现的情况。我们从外环结果趋同限度内元估计值差异减少中得出无药可治的界限。我们用数据驱动的代用模型和偏向密度展示了元估计值,用磁带聚变引发的不确定性下的一个设计问题,即优化恒星合点设计以尽量扩大高能粒子的估计封闭量。元估计值超出其全部减少变异技术本身,最终产生两个数量级的加速度,而在同一计算预算中与标准蒙特卡洛估算值相比,得出两个数量级的加速度。