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Physical invariance in neural networks for subgrid-scale scalar flux modeling

Abstract : In this paper we present a new strategy to model the subgrid-scale scalar flux in a three-dimensional turbulent incompressible flow using physics-informed neural networks (NNs). When trained from direct numerical simulation (DNS) data, state-of-the-art neural networks, such as convolutional neural networks, may not preserve well known physical priors, which may in turn question their application to real case-studies. To address this issue, we investigate hard and soft constraints into the model based on classical invariances and symmetries derived from physical laws. From simulation-based experiments, we show that the proposed physically-invariant NN model outperforms both purely data-driven ones as well as parametric state-of-the-art subgrid-scale model. The considered invariances are regarded as regularizers on physical metrics during the a priori evaluation and constrain the distribution tails of the predicted subgrid-scale term to be closer to the DNS. They also increase the stability and performance of the model when used as a surrogate during a large-eddy simulation. Moreover, the physically-invariant NN is shown to generalize to configurations that have not been seen during the training phase.
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https://hal.archives-ouvertes.fr/hal-03084215
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Submitted on : Tuesday, January 11, 2022 - 5:35:44 PM
Last modification on : Friday, January 14, 2022 - 3:36:35 AM

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2010.04663.pdf
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Hugo Frezat, Guillaume Balarac, Julien Le Sommer, Ronan Fablet, Redouane Lguensat. Physical invariance in neural networks for subgrid-scale scalar flux modeling. Physical Review Fluids, American Physical Society, 2021, 6 (2), ⟨10.1103/PhysRevFluids.6.024607⟩. ⟨hal-03084215v2⟩

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