ABSTRACT
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 to 10× finer resolution in each spatial dimension, resulting in 40- to 80-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.
ABSTRACT
A hybrid data-driven/finite volume method for 2D and 3D thermal convective flows is introduced. The approach relies on a single-step loss, convolutional neural network that is active only in the near-wall region of the flow. We demonstrate that the method significantly reduces errors in the prediction of the heat flux over the long-time horizon and increases pointwise accuracy in coarse simulations, when compared to direct computations on the same grids with and without a traditional subgrid model. We trace the success of our machine learning model to the choice of the training procedure, incorporating both the temporal flow development and distributional bias.