基于高斯混合的无监督机器学习检查点重启算法
An unsupervised machine-learning checkpoint-restart algorithm using Gaussian mixtures for particle-in-cell simulations
摘要：
提出了一种基于高斯混合粒子（PIC）算法的无监督机器学习检查点重启（CR）算法。该算法的特点是粒子压缩阶段和粒子重建阶段，在连续的粒子分布函数（PDF）的构造和重采样，分别。为了保证CR过程的保真度，我们确保在网格上的任何地方都精确保留压缩和重建阶段的不变量，如电荷、动量和能量。我们还确保了粒子重构后高斯定律的保持。其结果是，GM CR算法被证明提供了一个干净的，保守的重启能力，同时可能提供数量级的节省输入/输出的要求。我们证明了该算法使用最近开发的能量和电荷守恒PIC算法，使用静电和电磁测试。测试表明，不仅是一个高保真CR的能力，而且其潜力，提高保真度的PIC解决方案，对于一个给定的粒子分辨率。
英文摘要：
We propose an unsupervised machine-learning checkpoint-restart (CR) algorithm for particle-in-cell (PIC) algorithms using Gaussian mixtures (GM). The algorithm features a particle compression stage and a particle reconstruction stage, where a continuum particle distribution function (PDF) is constructed and resampled, respectively. To guarantee fidelity of the CR process, we ensure the exact preservation of invariants such as charge, momentum, and energy for both compression and reconstruction stages, everywhere on the mesh. We also ensure the preservation of Gauss' law after particle reconstruction. As a result, the GM CR algorithm is shown to provide a clean, conservative restart capability while potentially affording orders of magnitude savings in input/output requirements. We demonstrate the algorithm using a recently developed exactly energy- and charge-conserving PIC algorithm using both electrostatic and electromagnetic tests. The tests demonstrate not only a high-fidelity CR capability, but also its potential for enhancing the fidelity of the PIC solution for a given particle resolution.
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