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- W3100666994 abstract "Algorithms based on deep neural networks (DNNs) have attracted increasing attention from the scientific computing community. DNN based algorithms are easy to implement, natural for nonlinear problems, and have shown great potential to overcome the curse of dimensionality. In this work, we utilize the multi-scale DNN-based algorithm (MscaleDNN) proposed by Liu, Cai and Xu (2020) to solve multi-scale elliptic problems with possible nonlinearity, for example, the p-Laplacian problem. We improve the MscaleDNN algorithm by a smooth and localized activation function. Several numerical examples of multi-scale elliptic problems with separable or non-separable scales in low-dimensional and high-dimensional Euclidean spaces are used to demonstrate the effectiveness and accuracy of the MscaleDNN numerical scheme." @default.
- W3100666994 created "2020-11-23" @default.
- W3100666994 creator A5061256224 @default.
- W3100666994 date "2020-06-01" @default.
- W3100666994 modified "2023-10-18" @default.
- W3100666994 title "A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales" @default.
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- W3100666994 doi "https://doi.org/10.4208/cicp.oa-2020-0187" @default.
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