Deep Surrogate for Direct Time Fluid Dynamics

Computational Fluid Dynamics solvers have benefited from strong developments for decades, being critical for many scientific and industrial applications. The downside of their great accuracy is a requirement for tremendous computational resources. In this short article, we present our on-going work to design a data-driven deep surrogate: a neural network that is trained to provide a quality solution to the Navier-Stokes equations for a given domain, initial and boundary conditions. The resulting surrogate is expected to substitute traditional solvers in a limited range of input conditions, and enable interactive parameter exploration, sensibility analysis, and digital twins. Some approaches to build data-driven surrogates mimic the solver iterative process, being trained to compute the fluid transition from a time step t to t+1. Other surrogates are trained to directly produce a time step t, and are called "direct time". Surrogates also differ in their approach to space discretization. If the mesh is a regular grid, CNNs can be used. Irregular meshes or particle-based approaches are more challenging, and can be addressed through some variations of graph neural networks (GNN). Our contribution is a novel direct time GNN architecture for irregular meshes. It consists of a succession of graphs of increasing size connected by spline convolutions. Early experiments with the Von Karman’s vortex street benchmark show that our architecture achieves small generalization errors (RMSE at about 10^-3) and is not subject to error accumulation along the trajectory.