We study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity Monte Carlo estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.

翻译：本研究探讨计算成本高昂模型的多保真度不确定性传播问题。特别地，我们考虑高保真度与低保真度模型在随机输入数量及其概率分布方面均存在参数化差异的一般情况，这些分布既可能以闭式形式已知，也可能通过样本提供。我们推导了新型多保真度蒙特卡洛估计器，其依赖于高保真度与低保真度模型之间的共享子空间，在该子空间中参数遵循相同概率分布（即标准高斯分布）。我们通过归一化流将不同概率分布映射至共同分布来构建共享空间，并结合线性与非线性降维技术——分别为主动子空间与自编码器——以捕捉模型变化最显著的子空间。随后，我们将现有低保真度模型与这些变换相结合，构建出与高保真度模型相关性增强的修正模型，从而获得方差缩减的多保真度蒙特卡洛估计器。一系列数值实验阐明了所提方法的特性与优势。