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

TL;DR

This paper presents meta estimators that combine multifidelity variance reduction techniques to significantly accelerate Monte Carlo simulations in stellarator coil design optimization for magnetic confinement fusion.

Contribution

Introduction of novel meta estimators that integrate multiple variance reduction methods for efficient Monte Carlo estimation in outer-loop design problems.

Findings

Meta estimators achieve up to 100x speedup over standard Monte Carlo.

They outperform individual variance reduction techniques in efficiency.

Demonstrated effectiveness in a magnetic confinement fusion application.

Abstract

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.