基于决策树的三维矩形六面体流动矩（DTMOF）方法
a Decision-Tree based Moment-of-Fluid (DTMOF) Method in 3D rectangular hexahedrons
摘要：
流体矩法是流体体积法与分段线性界面法的推广。通过最小化切割多面体质心的最小二乘误差，MOF方法重建线性界面，而不使用任何相邻信息。传统的MOF涉及迭代，同时找到优化的线性重建。在这里，我们提出了一种基于机器学习算法的替代方法：决策树算法。训练数据集是从单位立方体的平面随机切割列表中生成的。决策树算法从训练数据中提取输入输出关系，使所得函数直接确定重建平面的法向量，无需任何迭代。目前的方法是测试一系列流行的界面平流测试问题。数值结果表明，我们的方法是比基于迭代的MOF方法快得多，同时提供兼容的精度与传统的MOF方法。
英文摘要：
The moment-of-fluid (MOF) method is an extension of the volume-of-fluid method with piecewise linear interface construction (VOF-PLIC). By minimizing the least square error of the centroid of the cutting polyhedron, the MOF method reconstructs the linear interface without using any neighboring information. Traditional MOF involves iteration while finding the optimized linear reconstruction. Here, we propose an alternative approach based on a machine learning algorithm: Decision Tree algorithm. A training data set is generated from a list of random cuts of a unit cube by plane. The Decision Tree algorithm extracts the input-output relationship from the training data, so that the resulting function determines the normal vector of the reconstruction plane directly, without any iteration. The present method is tested on a range of popular interface advection test problems. Numerical results show that our approach is much faster than the iteration-based MOF method while provides compatible accuracy with the conventional MOF method.
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