Fourier neural operators for spatiotemporal dynamics in two-dimensional turbulence

TL;DR

This paper explores the use of Fourier neural operators combined with PDE solvers to accelerate large-scale turbulence simulations, addressing computational challenges and data requirements for stable long-term predictions.

Contribution

It demonstrates how FNO models integrated with PDE solvers can improve turbulence simulation efficiency and discusses data and resolution considerations for effective modeling.

Findings

FNO models can accelerate turbulence simulations.

Integration with PDE solvers enhances stability for long-term predictions.

Identifies data volume and resolution needs for effective FNO training.

Abstract

High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational cost even though they become unstable or unphysical for long time predictions. We identify that the Fourier neural operator (FNO) based models combined with a partial differential equation (PDE) solver can accelerate fluid dynamic simulations and thus address computational expense of large-scale turbulence simulations. We treat the FNO model on the same footing as a PDE solver and answer important questions about the volume and temporal resolution of data required to build pre-trained models for turbulence. We also discuss the pitfalls of purely data-driven approaches that need to be avoided by the machine learning models to become viable and competitive tools for long time simulations of turbulence.