Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques
- Stanford Univ., CA (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- University of Notre Dame, IN (United States)
Here, 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 estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.
- Research Organization:
- Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- NA0003525
- OSTI ID:
- 2372957
- Report Number(s):
- SAND--2024-07517J
- Journal Information:
- Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 429; ISSN 0045-7825
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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