A multiscale neural network based on hierarchical matrices

5 Jul 2018  ·  Yuwei Fan, Lin Lin, Lexing Ying, Leonardo Zepeda-Nunez ·

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 Schr\"odinger equations and the Kohn-Sham density functional theory. read more

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Numerical Analysis