Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physics

2026-07-04

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Hojin Kim *

Varun Shankar

Venkatasubramanian Viswanathan

Romit Maulik

DOI：10.1016/j.compfluid.2026.107200

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Differentiable physical simulators are emerging as powerful tools for integrating machine learning (ML) models directly within computational fluid dynamics (CFD) solvers, enabling fully end-to-end training under physical constraints. In this work, we present a differentiable finite element framework for the incompressible Navier–Stokes equations, in which a graph neural network (GNN) is embedded as a subgrid-scale (SGS) closure and trained through the solver via discrete adjoint-based differentiation. We demonstrate the proposed approach on turbulent flow over a three-dimensional backward-facing step, a canonical separated-flow configuration. The learned GNN-based closure exhibits low prediction error, long-term numerical stability, and accurate recovery of key near-wall turbulence statistics, while preserving multiscale turbulent structures. Importantly, the model generalizes robustly to previously unseen geometries without retraining, highlighting its geometric adaptability on unstructured domains. Furthermore, we show that our GNN-based SGS models can be learned in a data-limited setting, using flowfield data from only a restricted subregion of the computational domain. These results demonstrate that end-to-end differentiable CFD provides a viable and scalable pathway toward physically consistent, stable, and generalizable data-driven turbulence closures on complex and unstructured domains.

Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physics

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