Coupling of the Finite Element Method with Physics Informed Neural Networks for the Multi-Fluid Flow Problem

TL;DR

This paper introduces a coupled finite element and physics-informed neural network approach to improve multi-fluid flow modeling, focusing on interface representation and capillary forces, validated through a rising bubble simulation.

Contribution

It presents a novel combined FEM-PINN discretization method and compares interface reinitialization techniques for multi-fluid flow problems.

Findings

PINN-FEM coupling improves interface accuracy

The proposed neural network architecture handles complex free surfaces

Validated on a rising bubble benchmark

Abstract

Multi-fluid flows are found in various industrial processes, including metal injection molding and 3D printing. The accuracy of multi-fluid flow modeling is determined by how well interfaces and capillary forces are represented. In this paper, the multi-fluid flow problem is discretized using a combination of a Physics-Informed Neural Network (PINN) with a finite element discretization. To determine the best PINN formulation, a comparative study is conducted using a manufactured solution. We compare interface reinitialization methods to determine the most suitable approach for our discretization strategy. We devise a neural network architecture that better handles complex free surface topologies. Finally, the coupled numerical strategy is used to model a rising bubble problem.