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

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arxiv 2309.11795 v1 pith:MH5O6OMD submitted 2023-09-21 math.NA cs.NA

L éo Bois , Emmanuel Franck , Laurent Navoret , Vincent Vigon This is my paper · ORCID
classification math.NAcs.NA
keywords controlartificialfunctiongalerkinlearningmethodoptimalproblem
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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 literatur

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