Differentiable Navier-Stokes Solvers for Turbulence-Aware Neural Surrogate Models

N. Meters, J. Lindqvist

We develop a fully differentiable spectral Navier-Stokes solver that enables end-to-end training of neural surrogate models for turbulent flows. Our approach embeds physical conservation laws directly into the computational graph, allowing gradient-based optimization to respect divergence-free constraints without projection steps. On the Kolmogorov flow benchmark, the resulting surrogates achieve 12x speedup over classical solvers at Reynolds numbers up to 10,000 with bounded error accumulation over 500 rollout steps.