Differentiable Hybrid Neural-CFD Modeling of Spatiotemporal Dynamics in 3D Wall-Bounded Turbulence

Accurately resolving wall-bounded turbulence at practical computational cost remains a central challenge in computational fluid dynamics (CFD). Traditional LES methods depend on subgrid-scale (SGS) closures and wall models to approximate unresolved dynamics, but their predictive accuracy degrades on coarse grids and in complex geometries. While machine learning has shown promise for modeling these effects a priori, achieving robust a posteriori accuracy remains elusive. In this work, we present a differentiable neural modeling framework that enables efficient, high-fidelity simulation of unsteady 3D wall-bounded turbulence on very coarse spatiotemporal resolutions. Our approach embeds deep neural operators into physics-based CFD solvers within a fully differentiable programming environment, allowing end-to-end training with gradient-based optimization. Specifically, the trainable neural components learn a unified closure strategy that captures subgrid stresses, wall shear, and discretization-induced numerical errors simultaneously. This integrated treatment ensures physical consistency, reduces reliance on large datasets, and improves generalization. Validation across test flow cases demonstrates that our framework delivers accurate spatiotemporal flow fields while significantly reducing computational cost. The results highlight the potential of differentiable physics and neural operator learning to advance surrogate modeling of spatiotemporal turbulence.