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

TL;DR

This paper presents a novel framework for embedding deep learning models, specifically graph neural networks, within finite element CFD solvers to develop stable, physically consistent, and generalizable turbulence closure models for complex unstructured domains.

Contribution

It introduces an end-to-end differentiable physics-based approach for data-driven turbulence modeling using GNNs within finite element solvers, applicable to complex 3D turbulent flows.

Findings

GNN-based closure achieves low prediction errors

Recovers key turbulence statistics and structures

Works in data-limited scenarios

Abstract

Differentiable physical simulators are proving to be valuable tools for developing data-driven models for computational fluid dynamics (CFD). In particular, these simulators enable end-to-end training of machine learning (ML) models embedded within CFD solvers. This paradigm enables novel algorithms which combine the generalization power and low cost of physics-based simulations with the flexibility and automation of deep learning methods. In this study, we introduce a framework for embedding deep learning models within a finite element solver for incompressible Navier-Stokes equations, specifically applying this approach to learn a subgrid-scale (SGS) closure with a graph neural network (GNN). We first demonstrate the feasibility of the approach on flow over a two-dimensional backward-facing step, using it as a proof of concept to show that solver-consistent training produces stable and physically meaningful closures. Then, we extend this to a turbulent flow over a three-dimensional backward-facing step. In this setting, the GNN-based closure not only attains low prediction errors, but also recovers key turbulence statistics and preserves multiscale turbulent structures. We further demonstrate that the closure can be identified in data-limited learning scenarios as well. Overall, the proposed end-to-end learning paradigm offers a viable pathway toward physically consistent and generalizable data-driven SGS modeling on complex and unstructured domains.