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

Journal Article · · Computer Methods in Applied Mechanics and Engineering

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

References (32)

The effects of clinically‐derived parametric data uncertainty in patient‐specific coronary simulations with deformable walls
  • Seo, Jongmin; Schiavazzi, Daniele E.; Kahn, Andrew M.
  • International Journal for Numerical Methods in Biomedical Engineering, Vol. 36, Issue 8 https://doi.org/10.1002/cnm.3351
journal June 2020
Multifidelity approaches for optimization under uncertainty: MULTIFIDELITY APPROACHES FOR OPTIMIZATION UNDER UNCERTAINTY journal September 2014
Multiscale modelling of the circulatory system: a preliminary analysis journal December 1999
Coupling between lumped and distributed models for blood flow problems journal December 2001
Patient-Specific Modeling of Blood Flow and Pressure in Human Coronary Arteries journal June 2010
Predictors of Myocardial Ischemia in Patients with Kawasaki Disease: Insights from Patient-Specific Simulations of Coronary Hemodynamics journal March 2023
Editorial: Special Issue on Verification, Validation, and Uncertainty Quantification of Cardiovascular Models: Towards Effective VVUQ for Translating Cardiovascular Modelling to Clinical Utility journal November 2018
On the one-dimensional theory of blood flow in the larger vessels journal October 1973
Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics journal June 2020
Multi-output multilevel best linear unbiased estimators via semidefinite programming journal August 2023
Multifidelity uncertainty quantification with models based on dissimilar parameters journal October 2023
Fast and robust parameter estimation with uncertainty quantification for the cardiac function journal April 2023
Basis adaptation in homogeneous chaos spaces journal February 2014
A generalized approximate control variate framework for multifidelity uncertainty quantification journal May 2020
On the optimization of approximate control variates with parametrically defined estimators journal February 2022
A cardiac electromechanical model coupled with a lumped-parameter model for closed-loop blood circulation journal May 2022
Variational inference with NoFAS: Normalizing flow with adaptive surrogate for computationally expensive models journal October 2022
The chemical basis of morphogenesis journal August 1952
Normalizing Flows: An Introduction and Review of Current Methods journal January 2020
Stationary Wave Solutions of a System of Reaction-Diffusion Equations Derived from the FitzHugh–Nagumo Equations journal February 1984
Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces journal January 2014
Optimal Model Management for Multifidelity Monte Carlo Estimation journal January 2016
Data-Driven Polynomial Ridge Approximation Using Variable Projection journal January 2018
Multifidelity Dimension Reduction via Active Subspaces journal January 2020
On Multilevel Best Linear Unbiased Estimators journal January 2020
Asymptotic Analysis of Multilevel Best Linear Unbiased Estimators journal January 2021
Multilevel Monte Carlo Path Simulation journal June 2008
Multifidelity Estimators for Coronary Circulation Models Under Clinically Informed data Uncertainty journal January 2020
normflows: A PyTorch Package for Normalizing Flows journal June 2023
Leveraging Intrinsic Principal Directions for Multifidelity Uncertainty Quantification report September 2018
A Surrogate Accelerated Bayesian Inverse Analysis of the HyShot II Flight Data conference April 2011
Recent advancements in Multilevel-Multifidelity techniques for forward UQ in the DARPA Sequoia project conference January 2019

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