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

Aaron B. Buhendwa, Stefan Adami, Nikolaus A. Adams
2021 Machine Learning with Applications  
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
more » ... rd 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. (N.A. Adams). from the observed data. For inference, PINN provide an alternative approach to traditional mesh-based methods for solving PDE from initial and boundary conditions, referred to as the forward problem. However, they also provide an arguably more attractive application, which is solving the inverse problem. In this case, potentially sparse and noisy data scattered across space and time of either auxiliary variables and/or some quantities of interest (QoI) are available. These data alongside the given physical laws are used to infer the entirety of the QoI within the whole spatio-temporal domain. The performance of PINN has been improved continuously. Lu et al. (2019) presented DeepXDE, which is a customizable python framework providing building blocks to construct individual problems regarding the spatio-temporal domain and boundary conditions. They proposed a new method to distribute the training points for the residual of the PDE (residual points). Analogously to adaptive refinement in meshbased solvers, residual points are added during training where the residua of the PDE is large, improving the efficiency of the training process. Dwivedi et al. (2019) proposed distributed PINN to evade the difficulty associated with training deep neural networks due to the well known problem of unstable and vanishing gradients (Pascanu et al., 2013) . Instead of using one potentially deep PINN for the whole spatio-temporal domain, the authors suggest to divide the domain into cells and locally install a PINN in each of these cells. To preserve global continuity and differentiability of the solution, it is necessary https://doi.
doi:10.1016/j.mlwa.2021.100029 fatcat:wvatvqgiqnap3fbs5yfnklwpd4