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

Journal Article · Tue Jan 31 00:00:00 EST 2023 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2023.115908· OSTI ID:2424931

Farcaș, Ionuț-Gabriel ^[1]; Peherstorfer, Benjamin ^[2]; Neckel, Tobias ^[3]; Jenko, Frank ^[4]; Bungartz, Hans-Joachim ^[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: US Air Force Office of Scientific Research (AFOSR); USDOE National Nuclear Security Administration (NNSA)
• 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: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
Context-aware learning
Model reduction
Multi-fidelity Monte Carlo
Nuclear fusion
Scientific machine learning