Physics-Constrained Neural Closure for Lattice Boltzmann Large-Eddy Simulation

We present a physics-constrained, data-driven subgrid-scale (SGS) stress closure for large-eddy simulation (LES) in the lattice Boltzmann method (LBM). Trained on filtered-downsampled (FD) data from LBM direct numerical simulation (DNS) of forced homogeneous isotropic turbulence (FHIT) spanning multiple filter widths, a compact neural network maps nine macroscopic derivative inputs - six strain-rate and three vorticity components - to the six independent components of the SGS stress tensor; a deviatoric projection is applied post-inference to obtain the traceless stress used in the solver. Training combines a stress data loss with physics terms for SGS energy-transfer (Pi) matching, rotational equivariance under cube rotations, and compatibility of the implied SGS forcing with the divergence-based coupling. The predicted stress is coupled to the solver through a split strategy: a dissipative, strain-aligned contribution is represented through an effective-viscosity projection, while the remaining anisotropic residual is applied through a forcing term. This construction is intended to retain both backscatter (via the effective viscosity) and non-dissipative anisotropic effects (via the residual forcing), while remaining compatible with LBM deployment. In the cases considered here, a priori results show good agreement with FD references across stress components and SGS-transfer statistics, and a posteriori rollouts improve several energetic and statistical measures relative to static and dynamic Smagorinsky baselines. A preliminary transfer test in turbulent channel flow is also reported without retraining. Finally, we demonstrate production deployment via ONNX Runtime, with throughput comparable to a dynamic Smagorinsky baseline in the tested configuration.