000232425 001__ 232425
000232425 005__ 20190317000855.0
000232425 022__ $$a0021-9991
000232425 0247_ $$a10.1016/j.jcp.2018.04.029$$2doi
000232425 037__ $$aARTICLE
000232425 245__ $$aAn artificial neural network as a troubled-cell indicator
000232425 260__ $$c2018
000232425 269__ $$a2018
000232425 336__ $$aJournal Articles
000232425 520__ $$aHigh-resolution schemes for conservation laws need to suitably limit the numerical solution near discontinuities, in order to avoid Gibbs oscillations. The solution quality and the computational cost of such schemes strongly depend on their ability to correctly identify troubled-cells, namely, cells where the solution loses regularity. Motivated by the objective to construct a universal troubled-cell indicator that can be used for general conservation laws, we propose a new approach to detect discontinuities using artificial neural networks (ANNs). In particular, we construct a multilayer perceptron (MLP), which is trained offline using a supervised learning strategy, and thereafter used as a black-box to identify troubled-cells. The proposed MLP indicator can accurately identify smooth extrema and is independent of problem-dependent parameters, which gives it an advantage over traditional limiter-based indicators. Several numerical results are presented to demonstrate the robustness of the MLP indicator in the framework of Runge-Kutta discontinuous Galerkin schemes, and its performance is compared with the minmod limiter and the minmod-based TVB limiter.
000232425 700__ $$g279450$$aRay, Deep$$0251026
000232425 700__ $$g232231$$aHesthaven, Jan S.$$0247428
000232425 773__ $$q166-191$$j367$$tJournal of computational physics
000232425 8560_ $$fjan.hesthaven@epfl.ch
000232425 8564_ $$uhttps://infoscience.epfl.ch/record/232425/files/nn_paper.pdf$$zPreprint$$s27436672$$yPreprint
000232425 8564_ $$uhttps://infoscience.epfl.ch/record/232425/files/manuscript_revised.pdf$$s1504269
000232425 8564_ $$uhttps://infoscience.epfl.ch/record/232425/files/manuscript_revised.pdf?subformat=pdfa$$s3465640$$xpdfa
000232425 909C0 $$xU12703$$0252492$$pMCSS
000232425 909CO $$ooai:infoscience.tind.io:232425$$qGLOBAL_SET$$pSB$$particle
000232425 917Z8 $$x232231
000232425 937__ $$aEPFL-ARTICLE-232425
000232425 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000232425 980__ $$aARTICLE