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We study the problem of multifidelity uncertainty propagation forcomputationally expensive models. In particular, we consider the generalsetting where the high-fidelity and low-fidelity models have a dissimilarparameterization both in terms of number of random inputs and their probabilitydistributions, which can be either known in closed form or provided throughsamples. We derive novel multifidelity Monte Carlo estimators which rely on ashared subspace between the high-fidelity and low-fidelity models where theparameters follow the same probability distribution, i.e., a standard Gaussian.We build the shared space employing normalizing flows to map differentprobability distributions into a common one, together with linear and nonlineardimensionality reduction techniques, active subspaces and autoencoders,respectively, which capture the subspaces where the models vary the most. Wethen compose the existing low-fidelity model with these transformations andconstruct modified models with an increased correlation with the high-fidelity,which therefore yield multifidelity Monte Carlo estimators with reducedvariance. A series of numerical experiments illustrate the properties andadvantages of our approaches.

Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques