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, 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：本文研究计算昂贵模型的多保真度不确定性传播问题。具体而言，我们考虑高保真度与低保真度模型在随机输入数量及概率分布（可闭式已知或通过样本提供）两方面均存在参数化差异的通用场景。我们推导出新型多保真度蒙特卡洛估计器，其核心在于构建高、低保真度模型共享的子空间——在该空间中参数服从相同概率分布（即标准高斯分布）。采用归一化流将不同概率分布映射至统一分布，同时结合线性降维技术（主动子空间）与非线性降维技术（自编码器）捕获模型变化最剧烈的子空间，从而构建该共享空间。进而对现有低保真度模型施加这些变换，构建与高保真度模型相关性增强的修正模型，由此获得方差缩减的多保真度蒙特卡洛估计器。系列数值实验验证了所提方法的特性与优势。