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• W2989600087 abstract "In this work we introduce a new multiscale artificial neural network based on the structure of $mathcal{H}$-matrices. This network generalizes the latter to the nonlinear case by introducing a local deep neural network at each spatial scale. Numerical results indicate that the network is able to efficiently approximate discrete nonlinear maps obtained from discretized nonlinear partial differential equations, such as those arising from nonlinear Schrödinger equations and the Kohn--Sham density functional theory." @default.
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• W2989600087 date "2019-01-01" @default.
• W2989600087 modified "2023-10-18" @default.
• W2989600087 title "A Multiscale Neural Network Based on Hierarchical Matrices" @default.
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• W2989600087 doi "https://doi.org/10.1137/18m1203602" @default.
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