Graph Neural Network Models of Multiphase Flow from Boundary Integral Methods

The suitability of graph convolutional neural networks for modeling multiphase flow through porous media is studied. The models are tasked with predicting interfacial velocity given fluid properties, such as capillary number, plus the location of fluid-fluid and fluid-solid particle interfaces as input. The networks are trained with data from high accuracy boundary integral simulations, a technique for simulating Newtonian flows at low Reynolds number, in which only the interface between fluid phases is meshed. The velocity at each collocation point is a function of all other points, so the adjacency matrix must be defined appropriately. When graph edges are weighted by inverse distance (within a cutoff), graph convolutional networks can encode the physics of multiphase flow interacting with solid obstacles, even without incorporating other physics-informed quantities, e.g., the curvature of the interface. Using graph convolutions with skip connections makes the use of very deep networks unnecessary. The performance of these optimized networks is compared to deep, densely connected neural networks and deep graph networks. The models developed in this work can accurately simulate interfacial flows two to three orders of magnitude faster than the original boundary integral simulations.