Current browse context:
physics.flu-dyn
Change to browse by:
References & Citations
Physics > Fluid Dynamics
Title: Differentiable Turbulence: Closure as a partial differential equation constrained optimization
(Submitted on 7 Jul 2023 (v1), last revised 27 Mar 2024 (this version, v2))
Abstract: Deep learning is increasingly becoming a promising pathway to improving the accuracy of sub-grid scale (SGS) turbulence closure models for large eddy simulations (LES). We leverage the concept of differentiable turbulence, whereby an end-to-end differentiable solver is used in combination with physics-inspired choices of deep learning architectures to learn highly effective and versatile SGS models for two-dimensional turbulent flow. We perform an in-depth analysis of the inductive biases in the chosen architectures, finding that the inclusion of small-scale non-local features is most critical to effective SGS modeling, while large-scale features can improve pointwise accuracy of the \textit{a-posteriori} solution field. The velocity gradient tensor on the LES grid can be mapped directly to the SGS stress via decomposition of the inputs and outputs into isotropic, deviatoric, and anti-symmetric components. We see that the model can generalize to a variety of flow configurations, including higher and lower Reynolds numbers and different forcing conditions. We show that the differentiable physics paradigm is more successful than offline, \textit{a-priori} learning, and that hybrid solver-in-the-loop approaches to deep learning offer an ideal balance between computational efficiency, accuracy, and generalization. Our experiments provide physics-based recommendations for deep-learning based SGS modeling for generalizable closure modeling of turbulence.
Submission history
From: Romit Maulik [view email][v1] Fri, 7 Jul 2023 15:51:55 GMT (1613kb,D)
[v2] Wed, 27 Mar 2024 23:15:33 GMT (2202kb,D)
Link back to: arXiv, form interface, contact.