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.

翻译：本文研究了一种混合技术，用于量化轴对称聚变反应堆中与磁平衡相关的自由边界问题在参数不确定性下数值解的变异性。该方法旨在通过将代理模型集成到多级蒙特卡洛方法中来降低计算成本。与涉及相关Grad-Shafranov偏微分方程直接数值求解的标准蒙特卡洛模拟相比，所得到的代理增强多级蒙特卡洛方法将模拟成本降低了高达$10^4$倍。精度评估还表明，基于代理模型的抽样结果与直接计算结果高度吻合，证实了其在捕捉等离子体边界和几何描述符行为方面的有效性。