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

arXiv: https://arxiv.org/abs/2101.09833 · HTML: https://mlsanity.com/paper/2101.09833/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 40 references that are in the map.
- First posted on arXiv 25 Jan 2021.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Deep Learning of Vortex Induced Vibrations](https://mlsanity.com/paper/1808.08952/) (2018)
- [Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks](https://mlsanity.com/paper/1909.12228/) (2019)

## Built on by (most cited first, 9 of 9)

- [JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows](https://mlsanity.com/paper/2203.13760/) (2022)
- [Partial Differential Equations Meet Deep Neural Networks: A Survey](https://mlsanity.com/paper/2211.05567/) (2022)
- [Physics-informed PointNet: On how many irregular geometries can it solve an inverse problem simultaneously? Application to linear elasticity](https://mlsanity.com/paper/2303.13634/) (2023)
- [JAX-Fluids 2.0: Towards HPC for Differentiable CFD of Compressible Two-phase Flows](https://mlsanity.com/paper/2402.05193/) (2024)
- [Solving the Discretised Multiphase Flow Equations with Interface Capturing on Structured Grids Using Machine Learning Libraries](https://mlsanity.com/paper/2401.06755/) (2024)
- [Physics-informed neural networks modeling for systems with moving immersed boundaries: application to an unsteady flow past a plunging foil](https://mlsanity.com/paper/2306.13395/) (2023)
- [Accelerating Simulation of Two-Phase Flows with Neural PDE Surrogates](https://mlsanity.com/paper/2405.17260/) (2024)
- [Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries](https://mlsanity.com/paper/2504.06327/) (2025)
- [Understanding the training of PINNs for unsteady flow past a plunging foil through the lens of input subdomain level loss function gradients](https://mlsanity.com/paper/2402.17346/) (2024)

## Abstract (arXiv)

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.