  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.
