Efficient global optimization (EGO) has become a standard approach for the global optimization of complex systems with high computational costs. EGO uses a training set of objective function values computed at selected input points to construct a statistical surrogate model, with low evaluation cost, on which the optimization procedure is applied. The training set is sequentially enriched, selecting new points, according to a prescribed infilling strategy, in order to converge to the optimum of the original costly model. Multifidelity approaches combining evaluations of the quantity of interest at different fidelity levels have been recently introduced to reduce the computational cost of building a global surrogate model. However, the use of multifidelity approaches in the context of EGO is still a research topic. In this work, we propose a new effective infilling strategy for multifidelity EGO. Our infilling strategy has the particularity of relying on non-nested training sets, a characteristic that comes with several computational benefits. For the enrichment of the multifidelity training set, the strategy selects the next input point together with the fidelity level of the objective function evaluation. This characteristic is in contrast with previous nested approaches, which require estimation of all lower fidelity levels and are more demanding to update the surrogate. The resulting EGO procedure achieves a significantly reduced computational cost, avoiding computations at useless fidelity levels whenever possible, but it is also more robust to low correlations between levels and noisy estimations. Analytical problems are used to test and illustrate the efficiency of the method. It is finally applied to the optimization of a fully nonlinear fluid-structure interaction system to demonstrate its feasibility on real large-scale problems, with fidelity levels mixing physical approximations in the constitutive models and discretization refinements.

中文翻译：

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基于多保真有效全局优化的非嵌套填充策略

高效全局优化（EGO）已成为具有高计算成本的复杂系统全局优化的标准方法。EGO使用在选定输入点处计算出的目标函数值的训练集来构建具有较低评估成本的统计替代模型，并在该模型上应用优化过程。根据规定的填充策略，依次丰富训练集，选择新点，以收敛到原始昂贵模型的最佳状态。最近引入了多保真度方法，该方法结合了对不同保真度级别的感兴趣数量的评估，以减少构建全局代理模型的计算成本。但是，在EGO中使用多保真方法仍然是一个研究主题。在这项工作中 我们为多元保真EGO提出了一种新的有效填充策略。我们的填充策略具有依赖于非嵌套训练集的特殊性，该特征具有多个计算优势。为了丰富多保真度训练集，该策略选择下一个输入点以及目标函数评估的保真度级别。该特性与以前的嵌套方法相反，后者需要估计所有较低的保真度级别，并且更需要更新代理。最终的EGO程序可显着降低计算成本，在任何可能的情况下都避免在无用的逼真度级别进行计算，但对于级别与噪声估计之间的低相关性，它也更加健壮。分析性问题用于测试和说明该方法的效率。最终将其应用于全非线性流固耦合系统的优化，以证明其在真实大规模问题上的可行性，保真度级别将本构模型中的物理近似值与离散化细化效果混合在一起。