Differentiable Turbulence: Closure as a partial differential equation constrained optimization

• URL: http://arxiv.org/abs/2307.03683v2
• Date: Wed, 27 Mar 2024 23:15:33 GMT
• Title: Differentiable Turbulence: Closure as a partial differential equation constrained optimization
• Authors: Varun Shankar, Dibyajyoti Chakraborty, Venkatasubramanian Viswanathan, Romit Maulik,
• Abstract summary: 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. We show that the differentiable physics paradigm is more successful than offline, textita-priori learning, and that hybrid solver-in-the-loop approaches to deep learning offer an ideal balance between computational efficiency, accuracy, and generalization.
• Score: 1.8749305679160366
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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