Differentiable Turbulence: Closure as a partial differential equation constrained optimization
arxiv(2023)
摘要
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 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, 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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