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Preprints, Working Papers, ... Year : 2023

An optimal control deep learning method to design artificial viscosities for Discontinuous Galerkin schemes

Une méthode de contrôle basée sur l'apprentissage pour construire des viscosités artificielles pour des schémas Galerkin Discontinus

Abstract

In this paper, we propose a method for constructing a neural network viscosity in order to reduce the non-physical oscillations generated by high-order Discontiuous Galerkin (DG) methods. To this end, the problem is reformulated as an optimal control problem for which the control is the viscosity function and the cost function involves comparison with a reference solution after several compositions of the scheme. The learning process is strongly based on gradient backpropagation tools. Numerical simulations show that the artificial viscosities constructed in this way are just as good or better than those used in the literature.
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Dates and versions

hal-04213057 , version 1 (21-09-2023)

Identifiers

  • HAL Id : hal-04213057 , version 1

Cite

Léo Bois, Emmanuel Franck, Laurent Navoret, Vincent Vigon. An optimal control deep learning method to design artificial viscosities for Discontinuous Galerkin schemes. 2023. ⟨hal-04213057⟩
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