  Numerical simulation of fluids plays an essential role in modeling many
physical phenomena, such as weather, climate, aerodynamics and plasma physics.
Fluids are well described by the Navier-Stokes equations, but solving these
equations at scale remains daunting, limited by the computational cost of
resolving the smallest spatiotemporal features. This leads to unfavorable
trade-offs between accuracy and tractability. Here we use end-to-end deep
learning to improve approximations inside computational fluid dynamics for
modeling two-dimensional turbulent flows. For both direct numerical simulation
of turbulence and large eddy simulation, our results are as accurate as
baseline solvers with 8-10x finer resolution in each spatial dimension,
resulting in 40-80x fold computational speedups. Our method remains stable
during long simulations, and generalizes to forcing functions and Reynolds
numbers outside of the flows where it is trained, in contrast to black box
machine learning approaches. Our approach exemplifies how scientific computing
can leverage machine learning and hardware accelerators to improve simulations
without sacrificing accuracy or generalization.
