用神经网络直接预测流体通量，省去传统界面重构步骤。
A 3D Machine Learning based Volume Of Fluid scheme without explicit interface reconstruction
- 用训练好的神经网络直接计算通量分数，不显式重构界面。
- 网格细化时数值收敛，精度优于两个基准方案。
- 适合需要高效模拟多材料流动的工程仿真场景。
我们提出一种基于机器学习的三维体积分数方法，用于模拟多材料流动。该方法的创新之处在于，通过预先训练的神经网络评估来计算通量分数，无需显式重构局部界面以逼近真实界面。网络在纯合成数据集上训练，该数据集通过随机采样大量局部界面生成，可根据需要调整以提升对非规则界面的处理能力。本文提出了若干确保方法效率及满足物理约束与性质的策略，并予以形式化。通过解决对流方程的数值实验，验证了该方法性能。当网格尺寸趋于零（h=1/N_h↓0）时，观察到数值收敛，且收敛速率优于两个基准方案。
原文摘要 · Abstract (English)
We present a machine-learning based Volume Of Fluid method to simulate multi-material flows on three-dimensional domains. One of the novelties of the method is that the flux fraction is computed by evaluating a previously trained neural network and without explicitly reconstructing any local interface approximating the exact one. The network is trained on a purely synthetic dataset generated by randomly sampling numerous local interfaces and which can be adapted to improve the scheme on less regular interfaces when needed. Several strategies to ensure the efficiency of the method and the satisfaction of physical constraints and properties are suggested and formalized. Numerical results on the advection equation are provided to show the performance of the method. We observe numerical convergence as the size of the mesh tends to zero $h=1/N_h\searrow 0$, with a better rate than two reference schemes.
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