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

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 n...

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Bibliographic Details
Published in:Physical review fluids 2021-02, Vol.6 (2), Article 024607
Main Authors: Frezat, Hugo, Balarac, Guillaume, Le Sommer, Julien, Fablet, Ronan, Lguensat, Redouane
Format: Article
Language:English
Subjects:
Computer Science
Engineering Sciences
Fluid Dynamics
Fluids mechanics
Machine Learning
Mechanics
Physics
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Summary: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.
ISSN:2469-990X
2469-990X
DOI:10.1103/PhysRevFluids.6.024607