EAGLE: LARGE-SCALE LEARNING OF TURBULENT FLUID DYNAMICS WITH MESH TRANSFORMERS

Abstract

Estimating fluid dynamics is classically done through the simulation and integration of numerical models solving the Navier-Stokes equations, which is computationally complex and time-consuming even on high-end hardware. This is a notoriously hard problem to solve, which has recently been addressed with machine learning, in particular graph neural networks (GNN) and variants trained and evaluated on datasets of static objects in static scenes with fixed geometry. We attempt to go beyond existing work in complexity and introduce a new model, method and benchmark. We propose EAGLE, a large-scale dataset of ∼1.1 million 2D meshes resulting from simulations of unsteady fluid dynamics caused by a moving flow source interacting with nonlinear scene structure, comprised of 600 different scenes of three different types. To perform future forecasting of pressure and velocity on the challenging EAGLE dataset, we introduce a new mesh transformer. It leverages node clustering, graph pooling and global attention to learn long-range dependencies between spatially distant data points without needing a large number of iterations, as existing GNN methods do. We show that our transformer outperforms state-of-the-art performance on, both, existing synthetic and real datasets and on EAGLE. Finally, we highlight that our approach learns to attend to airflow, integrating complex information in a single iteration.

1. INTRODUCTION

Despite consistently being at the center of attention of mathematics and computational physics, solving the Navier-Stokes equations governing fluid mechanics remains an open problem. In the absence of an analytical solution, fluid simulations are obtained by spatially and temporally discretizing differential equations, for instance with the finite volume or finite elements method. These simulations are computationally intensive, take up to several weeks for complex problems and require expert configurations of numerical solvers. Neural network-based physics simulators may represent a convenient substitute in many ways. Beyond the expected speed gain, their differentiability would allow for direct optimization of fluid mechanics problems (airplane profiles, turbulence resistance, etc.), opening the way to replace traditional trial-and-error approaches. They would also be an alternative for solving complex PDEs where numerical resolution is intractable. Yet, the development of such models is slowed down by the difficulty of collecting data in sufficient quantities to reach generalization. Velocity and pressure field measurements on real world systems require large and expensive devices, and simulation faces the problems described above. For all these reasons, few datasets are freely available for training highcapacity neural networks, and the existing ones either address relatively simple problems which can be simulated in reasonable time and exhibiting very similar behaviors (2D flow on a cylinder, airfoil

