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

TL;DR

This paper introduces advanced multifidelity Monte Carlo estimators that leverage normalizing flows and dimensionality reduction to improve uncertainty propagation in complex models with dissimilar parameterizations.

Contribution

It presents novel estimators using shared subspaces created by normalizing flows and dimensionality reduction, enhancing correlation between models for variance reduction.

Findings

Reduced variance in Monte Carlo estimators

Effective handling of dissimilar parameterizations

Improved accuracy in uncertainty propagation

Abstract

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.