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

• Published in: Machine learning with applications 2021-06, Vol.4, p.100029, Article 100029
• Main Authors: Buhendwa, Aaron B., Adami, Stefan, Adams, Nikolaus A.
• Format: Article
• Language: English
• Subjects: Hidden fluid mechanics; Incompressible Navier–Stokes equations; Physics-informed neural networks; Two-phase flows; Volume-of-fluid
• ISSN: 2666-8270; 2666-8270
• DOI: 10.1016/j.mlwa.2021.100029

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. •We infer flow fields from scattered-time data of the interface position.•We present an effective way to distribute the training points.•We give insight into the proper choice of hyperparameters.•The use of global and local adaptive activation functions is evaluated.