Deep Surrogate for Direct Time Fluid Dynamics

TL;DR

This paper introduces a novel graph neural network architecture designed for direct time fluid dynamics simulation on irregular meshes, aiming to improve accuracy and reduce error accumulation compared to existing surrogate models.

Contribution

The paper proposes a new direct time GNN architecture with spline convolutions for irregular meshes, demonstrating promising results on a fluid dynamics benchmark.

Findings

Achieves small generalization errors

Mitigates error accumulation along trajectories

Effective on Von Kármán's vortex street benchmark

Abstract

The ubiquity of fluids in the physical world explains the need to accurately simulate their dynamics for many scientific and engineering applications. Traditionally, well established but resource intensive CFD solvers provide such simulations. The recent years have seen a surge of deep learning surrogate models substituting these solvers to alleviate the simulation process. Some approaches to build data-driven surrogates mimic the solver iterative process. They infer the next state of the fluid given its previous one. Others directly infer the state from time input. Approaches also differ in their management of the spatial information. Graph Neural Networks (GNN) can address the specificity of the irregular meshes commonly used in CFD simulations. In this article, we present our ongoing work to design a novel direct time GNN architecture for irregular meshes. It consists of a succession of graphs of increasing size connected by spline convolutions. We test our architecture on the Von K{\'a}rm{\'a}n's vortex street benchmark. It achieves small generalization errors while mitigating error accumulation along the trajectory.