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Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification

Journal Article · · Computer Methods in Applied Mechanics and Engineering
 [1];  [2];  [3];  [4];  [3]
  1. Univ. of Texas, Austin, TX (United States)
  2. New York Univ. (NYU), NY (United States)
  3. Technical Univ. of Munich (Germany)
  4. Max Planck Institute for Plasma Physics, Garching (Germany); Univ. of Texas, Austin, TX (United States); Technical Univ. of Munich (Germany)

Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is computationally expensive. This work proposes a context-aware multi-fidelity Monte Carlo method that optimally balances the costs of training low-fidelity models with the costs of Monte Carlo sampling. It generalizes the previously developed context-aware bi-fidelity Monte Carlo method to hierarchies of multiple models and to more general types of low-fidelity models. When training low-fidelity models, the proposed approach takes into account the context in which the learned low-fidelity models will be used, namely for variance reduction in Monte Carlo estimation, which allows it to find optimal trade-offs between training and sampling to minimize upper bounds of the mean-squared errors of the estimators for given computational budgets. This is in stark contrast to traditional surrogate modeling and model reduction techniques that construct low-fidelity models with the primary goal of approximating well the high-fidelity model outputs and typically ignore the context in which the learned models will be used in upstream tasks. Further, the proposed context-aware multi-fidelity Monte Carlo method applies to hierarchies of a wide range of types of low-fidelity models such as sparse-grid and deep-network models. Numerical experiments with the gyrokinetic simulation code Gene show speedups of up to two orders of magnitude compared to standard estimators when quantifying uncertainties in small-scale fluctuations in confined plasma in fusion reactors. This corresponds to a runtime reduction from 72 days to four hours on one node of the Lonestar6 supercomputer at the Texas Advanced Computing Center.

Research Organization:
US Department of Energy (USDOE), Washington, DC (United States). Office of Science, Exascale Computing Project
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); US Air Force Office of Scientific Research (AFOSR)
OSTI ID:
2424931
Alternate ID(s):
OSTI ID: 1923121
Journal Information:
Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 406; ISSN 0045-7825
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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