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

Hugo Frezat*

Guillaume Balarac

Julien Le Sommer

Ronan Fablet

Redouane Lguensat

  • University Grenoble Alpes, CNRS UMR LEGI, Grenoble, France

  • University Grenoble Alpes, CNRS UMR LEGI, Grenoble, France and Institut Universitaire de France (IUF), Paris, France

  • University Grenoble Alpes, CNRS UMR IGE, Grenoble, France

  • IMT Atlantique, CNRS UMR Lab-STICC, Brest, France

  • Laboratoire des Sciences du Climat et de l'Environnement (LSCE), IPSL/CEA, Gif Sur Yvette, France and LOCEAN-IPSL, Sorbonne Université, Institut Pierre Simon Laplace, Paris, France

  • *hugo.frezat@univ-grenoble-alpes.fr
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Phys. Rev. Fluids 6, 024607 – Published 22 February, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.024607

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 transformation invariances and symmetries derived from physical laws. From simulation-based experiments, we show that the proposed transformation-invariant NN model outperforms both purely data-driven ones as well as parametric state-of-the-art subgrid-scale models. 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 transformation-invariant NN is shown to generalize to regimes that have not been seen during the training phase.

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Corrections

18 March, 2021

Correction: References [3] and [15] were updated incorrectly at the proof stage and have been fixed. A reference citation below Eq. (14) has been fixed.

Article Text

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Outline

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Phys. Rev. Fluids 6, 024607– Published 22 February, 2021
  • Received 12 October 2020
  • Accepted 1 February 2021
  • Corrected 18 March 2021
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