基于代理模型的多级蒙特卡洛方法用于等离子体边界问题的不确定性量化
Surrogate-based multilevel Monte Carlo methods for uncertainty quantification in the Grad-Shafranov free boundary problem
AI总结：
本文提出基于代理模型的多级蒙特卡洛方法，用于高效量化等离子体边界问题的不确定性，显著降低计算成本并验证方法有效性。
摘要：
我们探索了一种混合技术，用于量化轴对称聚变反应堆中磁平衡自由边界问题数值解的变异性，同时考虑参数不确定性。该方法旨在通过将代理模型整合到多级蒙特卡洛方法中来降低计算成本。所得到的代理增强型多级蒙特卡洛方法将模拟成本降低了高达$10^4$倍，相比直接求解相关格拉-沙弗兰诺夫偏微分方程的标准蒙特卡洛模拟。准确性评估也显示，基于代理的采样结果与直接计算结果高度一致，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。
英文摘要：
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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