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arXiv · 2202.09488

An Operator Learning Approach via Function-valued Reproducing Kernel Hilbert Space for Differential Equations

Kaijun Bao·Xu Qian·Ziyuan Liu·Songhe Song
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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.

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Kaijun Bao, Xu Qian, Ziyuan Liu, Songhe Song. 2022-02-19. An Operator Learning Approach via Function-valued Reproducing Kernel Hilbert Space for Differential Equations. https://arxiv.org/abs/2202.09488

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