Machine learning accelerated computational fluid dynamics

Numerical simulations of fluids, such as those used for weather and climate modeling, are limited by the trade-off between computational cost and grid resolution. Traditional methods require extremely fine meshes to resolve the smallest spatiotemporal scales (Kolmogorov scales) of turbulent flows, making high-fidelity simulations prohibitively expensive at scale. This paper asks whether deep learning can be used to augment numerical solvers, allowing for accurate simulations on significantly coarser grids without sacrificing stability or generalization.

The authors propose a data-driven discretization method where neural networks are embedded directly into a traditional finite-volume CFD solver. Instead of using black-box machine learning to replace the entire simulation, the authors use convolutional neural networks to replace only the specific components most affected by resolution loss—namely, the interpolation of convective fluxes. By training this hybrid system using high-resolution ground truth data through differentiable programming (JAX), the model learns local operators that enforce physical consistency and symmetry, which are often absent in pure ML approaches.

The researchers demonstrate that their learned interpolation method effectively behaves like a high-resolution solver despite using a 10x coarser grid in each spatial dimension. For two-dimensional Kolmogorov flow, the model maintains pointwise accuracy comparable to direct numerical simulation (DNS) while delivering 40-80x speedups on hardware accelerators. Crucially, the model demonstrates strong generalization capabilities: it maintains accuracy when applied to different forcing functions, larger spatial domains, and higher Reynolds numbers than those seen during training. This is a significant advantage over purely data-driven ML baselines, which often fail to generalize or remain stable during long-term simulation.