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

arXiv: https://arxiv.org/abs/2312.12361 · HTML: https://mlsanity.com/paper/2312.12361/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2023.

## Built on by (most cited first, 6 of 6)

- [Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiology](https://mlsanity.com/paper/2408.07201/) (2024)
- [Neural active manifolds: nonlinear dimensionality reduction for uncertainty quantification](https://mlsanity.com/paper/2408.03534/) (2024)
- [Enabling stratified sampling in high dimensions via nonlinear dimensionality reduction](https://mlsanity.com/paper/2506.08921/) (2025)
- [On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiological boundary conditions](https://mlsanity.com/paper/2506.11683/) (2025)
- [Data-Driven Bifurcation Handling in Physics-Based Reduced-Order Vascular Hemodynamic Models](https://mlsanity.com/paper/2508.21165/) (2025)
- [FalconBC: Flow matching for Amortized inference of Latent-CONditioned physiologic Boundary Conditions](https://mlsanity.com/paper/2603.19331/) (2026)

## Abstract (arXiv)

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.