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

Howard Elman; Jiaxing Liang; Tonatiuh Sánchez-Vizuet

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arXiv · 2501.08482

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

Howard Elman·Jiaxing Liang·Tonatiuh Sánchez-Vizuet

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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.

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Howard Elman, Jiaxing Liang, Tonatiuh Sánchez-Vizuet. 2026-03-01. Surrogate-based multilevel Monte Carlo methods for uncertainty quantification in the Grad-Shafranov free boundary problem. https://arxiv.org/abs/2501.08482

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