Data-driven low-fidelity models for multi-fidelity Monte Carlo sampling in plasma micro-turbulence analysis
Data-driven low-fidelity models for multi-fidelity Monte Carlo sampling in plasma micro-turbulence analysis
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DOI：
10.1016/j.jcp.2021.110898
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发表时间：
2021-03
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通讯作者：
J. Konrad;Ionut-Gabriel Farcas;B. Peherstorfer;A. Siena;F. Jenko;T. Neckel;H. Bungartz
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作者：
J. Konrad;Ionut-Gabriel Farcas;B. Peherstorfer;A. Siena;F. Jenko;T. Neckel;H. Bungartz
已知磁化聚变等离子体中驱动湍流传输的线性微不稳定性（以及相应的非线性饱和机制）对于表征背景等离子体和磁平衡的各种物理参数很敏感。因此，不确定性量化对于实现等离子体湍流的预测数值模拟至关重要。然而，所需的回旋运动模拟的高计算成本和大量参数使得标准蒙特卡罗技术变得棘手。为了解决这个问题，我们提出了一种多保真蒙特卡罗方法，其中我们采用数据驱动的低保真模型，该模型利用潜在问题的结构，例如低内在维度和随机输入的各向异性耦合。使用全套不确定输入和仅包含选定的重要参数的子集，通过灵敏度驱动的维度自适应稀疏网格插值有效地构建低保真模型。我们通过将该方法应用于具有多达 14 个随机参数的两个等离子体湍流问题来说明该方法的强大功能，证明该方法比单核性能测量的标准蒙特卡洛方法效率高出四个数量级，这意味着在并行计算机上的 240 个核心上，运行时间从大约 8 天减少到 1 小时。
The linear micro-instabilities driving turbulent transport in magnetized fusion plasmas (as well as the respective nonlinear saturation mechanisms) are known to be sensitive with respect to various physical parameters characterizing the background plasma and the magnetic equilibrium. Therefore, uncertainty quantification is essential for achieving predictive numerical simulations of plasma turbulence. However, the high computational costs of the required gyrokinetic simulations and the large number of parameters render standard Monte Carlo techniques intractable. To address this problem, we propose a multi-fidelity Monte Carlo approach in which we employ data-driven low-fidelity models that exploit the structure of the underlying problem such as low intrinsic dimension and anisotropic coupling of the stochastic inputs. The low-fidelity models are efficiently constructed via sensitivity-driven dimension-adaptive sparse grid interpolation using both the full set of uncertain inputs and subsets comprising only selected, important parameters. We illustrate the power of this method by applying it to two plasma turbulence problems with up to 14 stochastic parameters, demonstrating that it is up to four orders of magnitude more efficient than standard Monte Carlo methods measured in single-core performance, which translates into a runtime reduction from around eight days to one hour on 240 cores on parallel machines.