Graph Neural Networks for Complex Fluid Simulations

Abstract

Traditionally, computational fluid dynamics expands on various numerical models that solve the Navier-Stokes equations. However, these methods often require significant computation time and resources. For example, the interaction between N particles requires O(N 2 ) evaluations, so cut-off radii or fittings onto a regular grid are usually introduced. Recently, machine learning, and specifically graph neural networks, have been used to address these challenges. Existing non-GNN-based methods widely resort to convolutional architectures on static grid geometry. Classical GNN-based approaches use a Lagrangian representation of fluids and construct graphs for each fluid particle with some fixed connectivity radius. These models, however, can not tolerate large time step sizes in training and prediction. Other GNN-based models are multi-scale GNN models which iteratively adapt unstructured meshes. They in turn suffer from connectivity loss when the mesh is coarsened and subsequently refined. We introduce a new hierarchical GNN architecture to create compact graph representations and consecutively learn physical interactions on this low-rank approximation. We leverage attention pooling to coarsen the input graph and include the spatial information into consideration. Our method compares to GNS [1] baseline on fluid dynamics prediction tasks and produces errors similar in magnitude. We demonstrate stable roll-outs and show steady predictions even for long roll-outs.