用多保真度蒙特卡罗加速仿星器中高能粒子约束统计的估计
Accelerating the estimation of energetic particle confinement statistics in stellarators using multifidelity Monte Carlo
摘要：
在仿星器的设计中，高能粒子约束是一个关键的问题，从数值的角度研究仍然具有挑战性。标准蒙特卡罗分析是非常昂贵的，因为大量的粒子轨迹需要在很长的时间尺度上进行积分，并且必须采取小的时间步长来准确地捕捉各种轨迹的特征。即使它们是基于引导中心轨道，而不是全轨道，这些标准的蒙特卡罗研究也太昂贵了，不能包括在大多数仿星器优化代码中。我们提出了第一个多保真度蒙特卡罗计划加速估计的高能粒子约束仿星器。我们的方法依赖于一个两级的层次结构，其中一个指导中心模型作为高保真度模型，和一个数据驱动的线性插值作为低保真度的代理模型。我们应用多保真度蒙特卡罗的研究充满活力的粒子约束在一个4周期的准螺旋对称仿星器，评估各种指标的约束。从我们的代理模型的计算效率非常高，以及其足够的相关性，高保真度模型，我们得到的加速比高达10与多保真度蒙特卡洛相比，标准蒙特卡洛。
英文摘要：
In the design of stellarators, energetic particle confinement is a critical point of concern which remains challenging to study from a numerical point of view. Standard Monte Carlo analyses are highly expensive because a large number of particle trajectories need to be integrated over long time scales, and small time steps must be taken to accurately capture the features of the wide variety of trajectories. Even when they are based on guiding center trajectories, as opposed to full-orbit trajectories, these standard Monte Carlo studies are too expensive to be included in most stellarator optimization codes. We present the first multifidelity Monte Carlo scheme for accelerating the estimation of energetic particle confinement in stellarators. Our approach relies on a two-level hierarchy, in which a guiding center model serves as the high-fidelity model, and a data-driven linear interpolant is leveraged as the low-fidelity surrogate model. We apply multifidelity Monte Carlo to the study of energetic particle confinement in a 4-period quasi-helically symmetric stellarator, assessing various metrics of confinement. Stemming from the very high computational efficiency of our surrogate model as well as its sufficient correlation to the high-fidelity model, we obtain speedups of up to 10 with multifidelity Monte Carlo compared to standard Monte Carlo.
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