Inferring incompressible two-phase flow fields from the interface motion using physics-informed neural networks

TL;DR

This paper demonstrates how physics-informed neural networks can effectively solve both forward and inverse two-phase flow problems, accurately inferring velocity and pressure fields from interface data, with strategies for improved training.

Contribution

It introduces a novel application of physics-informed neural networks to two-phase flow, including methods for interface data fitting and loss weighting, enhancing inverse problem solutions.

Findings

Successful inference of velocity and pressure fields from interface data.

Effective training strategies for interface fitting and residual loss weighting.

Evaluation of adaptive activation functions improves model performance.

Abstract

In this work, physics-informed neural networks are applied to incompressible two-phase flow problems. We investigate the forward problem, where the governing equations are solved from initial and boundary conditions, as well as the inverse problem, where continuous velocity and pressure fields are inferred from scattered-time data on the interface position. We employ a volume of fluid approach, i.e. the auxiliary variable here is the volume fraction of the fluids within each phase. For the forward problem, we solve the two-phase Couette and Poiseuille flow. For the inverse problem, three classical test cases for two-phase modeling are investigated: (i) drop in a shear flow, (ii) oscillating drop and (iii) rising bubble. Data of the interface position over time is generated by numerical simulation. An effective way to distribute spatial training points to fit the interface, i.e. the volume fraction field, and the residual points is proposed. Furthermore, we show that appropriate weighting of losses associated with the residual of the partial differential equations is crucial for successful training. The benefit of using adaptive activation functions is evaluated for both the forward and inverse problem.