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

Ionuț Gabriel Farcaș, Benjamin Peherstorfer, Tobias Neckel, Frank Jenko, Hans Joachim Bungartz

Research output: Contribution to journalArticlepeer-review


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. 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.

Original languageEnglish (US)
Article number115908
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Mar 1 2023


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

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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