Fourier neural operators for spatiotemporal dynamics in two-dimensional turbulence
This work addresses computational expense for researchers and engineers in fluid dynamics, offering an incremental improvement over existing machine learning approaches.
The paper tackles the computational challenge of high-fidelity turbulence simulations by combining Fourier neural operators (FNO) with PDE solvers to accelerate fluid dynamics, addressing data requirements and pitfalls of purely data-driven methods for long-term stability.
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.