Meta variance reduction for Monte Carlo estimation of energetic particle confinement during stellarator optimization

Frederick Law, Antoine Cerfon, Benjamin Peherstorfer, Florian Wechsung

Research output: Contribution to journalArticlepeer-review


This work introduces meta estimators that combine multiple multifidelity techniques based on control variates, importance sampling, and information reuse to yield a quasi-multiplicative amount of variance reduction. The proposed meta estimators are particularly efficient within outer-loop applications when the input distribution of the uncertainties changes during the outer loop, which is often the case in reliability-based design and shape optimization. We derive asymptotic bounds of the variance reduction of the meta estimators in the limit of convergence of the outer-loop results. We demonstrate the meta estimators, using data-driven surrogate models and biasing densities, on a design problem under uncertainty motivated by magnetic confinement fusion, namely the optimization of stellarator coil designs to maximize the estimated confinement of energetic particles. The meta estimators outperform all of their constituent variance reduction techniques alone, ultimately yielding two orders of magnitude speedup compared to standard Monte Carlo estimation at the same computational budget.

Original languageEnglish (US)
Article number112524
JournalJournal of Computational Physics
StatePublished - Dec 15 2023


  • Design under uncertainty
  • Model reduction
  • Monte Carlo methods
  • Multifidelity methods
  • Surrogate modeling

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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