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- W4224317045 abstract "Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert spaces in our operator learning model. We use neural networks to parameterize Hilbert-Schmidt integral operator and propose an architecture. Experiments including several typical datasets show that the proposed architecture has desirable accuracy on linear and nonlinear partial differential equations even with a small amount of data. By learning the mappings between function spaces, the proposed method can find the solution of a high-resolution input after learning from lower-resolution data." @default.
- W4224317045 created "2022-04-26" @default.
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- W4224317045 date "2022-02-18" @default.
- W4224317045 modified "2023-09-28" @default.
- W4224317045 title "An Operator Learning Approach via Function-valued Reproducing Kernel Hilbert Space for Differential Equations" @default.
- W4224317045 doi "https://doi.org/10.48550/arxiv.2202.09488" @default.
- W4224317045 hasPublicationYear "2022" @default.
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