%0 Generic %1 fan2018multiscale %A Fan, Yuwei %A Lin, Lin %A Ying, Lexing %A Zepeda-Nunez, Leonardo %D 2018 %K multiresolution spatial todo:read %T A multiscale neural network based on hierarchical matrices %U http://arxiv.org/abs/1807.01883 %X In this work we introduce a new multiscale artificial neural network based on the structure of $H$-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.

@misc{fan2018multiscale, 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 Schr\"odinger equations and the Kohn-Sham density functional theory.}, added-at = {2022-06-20T11:16:07.000+0200}, author = {Fan, Yuwei and Lin, Lin and Ying, Lexing and Zepeda-Nunez, Leonardo}, biburl = {https://www.bibsonomy.org/bibtex/2b4ae3d0b04527716d6865e830b0c22db/annakrause}, description = {1807.01883.pdf}, interhash = {ffd9940f9cccd6bd2c6c571a77f39d62}, intrahash = {b4ae3d0b04527716d6865e830b0c22db}, keywords = {multiresolution spatial todo:read}, note = {cite arxiv:1807.01883Comment: 26 pages, 11 figures}, timestamp = {2022-06-20T11:16:07.000+0200}, title = {A multiscale neural network based on hierarchical matrices}, url = {http://arxiv.org/abs/1807.01883}, year = 2018 }