Surrogate-based multilevel Monte Carlo methods for uncertainty quantification in the Grad-Shafranov free boundary problem

TL;DR

This paper introduces a surrogate-enhanced multilevel Monte Carlo method that significantly reduces computational costs in uncertainty quantification for the Grad-Shafranov free boundary problem in fusion reactors, maintaining high accuracy.

Contribution

The paper presents a novel hybrid approach combining surrogate models with multilevel Monte Carlo to efficiently quantify uncertainties in plasma boundary simulations.

Findings

Cost reduction by up to 10^4 times compared to standard Monte Carlo methods.

High accuracy in capturing plasma boundary behavior.

Effective uncertainty quantification in fusion reactor models.

Abstract

We explore a hybrid technique to quantify the variability in the numerical solutions to a free boundary problem associated with magnetic equilibrium in axisymmetric fusion reactors amidst parameter uncertainties. The method aims at reducing computational costs by integrating a surrogate model into a multilevel Monte Carlo method. The resulting surrogate-enhanced multilevel Monte Carlo methods reduce the cost of simulation by factors as large as $10^4$ compared to standard Monte Carlo simulations involving direct numerical solutions of the associated Grad-Shafranov partial differential equation. Accuracy assessments also show that surrogate-based sampling closely aligns with the results of direct computation, confirming its effectiveness in capturing the behavior of plasma boundary and geometric descriptors.