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

• URL: http://arxiv.org/abs/2307.13533v2
• Date: Fri, 22 Nov 2024 19:02:10 GMT
• Title: Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physics
• Authors: Hojin Kim, Varun Shankar, Venkatasubramanian Viswanathan, Romit Maulik,
• Abstract summary: We introduce a framework for embedding deep learning models within a generic finite element solver to solve the Navier-Stokes equations. We validate our method for flow over a backwards-facing step and test its performance on novel geometries. We show that our GNN-based closure model may be learned in a data-limited scenario by interpreting closure modeling as a solver-constrained optimization.
• Score: 1.8749305679160366
• License:
• Abstract: Differentiable physical simulators are proving to be valuable tools for developing data-driven models in computational fluid dynamics (CFD). 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 generic finite element solver to solve the Navier-Stokes equations, specifically applying this approach to learn a subgrid scale closure with a graph neural network (GNN). We validate our method for flow over a backwards-facing step and test its performance on novel geometries, demonstrating the ability to generalize to novel geometries without sacrificing stability. Additionally, we show that our GNN-based closure model may be learned in a data-limited scenario by interpreting closure modeling as a solver-constrained optimization. Our end-to-end learning paradigm demonstrates a viable pathway for physically consistent and generalizable data-driven closure modeling across complex geometries.

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