Learned Coarse Models for Efficient Turbulence Simulation

TL;DR

This paper introduces a learned turbulence simulator that outperforms classical numerical solvers at low resolutions, capturing complex turbulent dynamics more accurately and with improved stability through simple training techniques.

Contribution

The authors develop a data-driven turbulence simulation model that surpasses traditional solvers in accuracy and stability at low resolutions, using a simple, end-to-end trained architecture.

Findings

Learned simulators outperform classical solvers at low resolutions.

Training noise and dataset augmentation improve stability and generalization.

The model accurately reproduces turbulent dynamics, including those from high-resolution data.

Abstract

Turbulence simulation with classical numerical solvers requires high-resolution grids to accurately resolve dynamics. Here we train learned simulators at low spatial and temporal resolutions to capture turbulent dynamics generated at high resolution. We show that our proposed model can simulate turbulent dynamics more accurately than classical numerical solvers at the comparably low resolutions across various scientifically relevant metrics. Our model is trained end-to-end from data and is capable of learning a range of challenging chaotic and turbulent dynamics at low resolution, including trajectories generated by the state-of-the-art Athena++ engine. We show that our simpler, general-purpose architecture outperforms various more specialized, turbulence-specific architectures from the learned turbulence simulation literature. In general, we see that learned simulators yield unstable trajectories; however, we show that tuning training noise and temporal downsampling solves this problem. We also find that while generalization beyond the training distribution is a challenge for learned models, training noise, added loss constraints, and dataset augmentation can help. Broadly, we conclude that our learned simulator outperforms traditional solvers run on coarser grids, and emphasize that simple design choices can offer stability and robust generalization.