This paper solves the multiphase flow equations with interface capturing using the AI4PDEs approach (Artificial Intelligence for Partial Differential Equations). The solver within AI4PDEs uses tools from machine learning (ML) libraries to solve (exactly) partial differential equations (PDEs) that have been discretised using numerical methods. Convolutional layers can be used to express the discretisations as a neural network, whose weights are determined by the numerical method, rather than by training. To solve the system, a multigrid solver is implemented through a neural network with a U-Net architecture. Immiscible two-phase flow is modelled by the 3D incompressible Navier-Stokes equations with surface tension and advection of a volume fraction field, which describes the interface between the fluids. A new compressive algebraic volume-of-fluids method is introduced, based on a residual formulation using Petrov-Galerkin for accuracy and designed with AI4PDEs in mind. High-order finite-element based schemes are chosen to model a collapsing water column and a rising bubble. Results compare well with experimental data and other numerical results from the literature, demonstrating that, for the first time, finite element discretisations of multiphase flows can be solved using the neural network solver from the AI4PDEs approach. A benefit of expressing numerical discretisations as neural networks is that the code can run, without modification, on CPUs, GPUs or the latest accelerators designed especially to run AI codes.

利用AI4PDEs方法解决多相流动方程与界面捕捉问题，通过神经网络求解数值离散化的偏微分方程，对多相流动进行建模，并在实验数据和文献结果上取得良好的比较，展示了AI4PDEs方法在有限元离散化的多相流动求解上的优势。

利用机器学习库在结构化网格上解决离散多相流方程并捕获界面