Deep Surrogate Model for Learning Green’s Function Associated with Linear Reaction-Diffusion Operator
Year: 2024
Author: Junqing Jia, Lili Ju, Xiaoping Zhang
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 5 : pp. 697–715
Abstract
In this paper, we present a deep surrogate model for learning the Green’s function associated with the reaction-diffusion operator in rectangular domain. The U-Net architecture is utilized to effectively capture the mapping from source to solution of the target partial differential equations (PDEs). To enable efficient training of the model without relying on labeled data, we propose a novel loss function that draws inspiration from traditional numerical methods used for solving PDEs. Furthermore, a hard encoding mechanism is employed to ensure that the predicted Green’s function is perfectly matched with the boundary conditions. Based on the learned Green’s function from the trained deep surrogate model, a fast solver is developed to solve the corresponding PDEs with different sources and boundary conditions. Various numerical examples are also provided to demonstrate the effectiveness of the proposed model.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1028
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 5 : pp. 697–715
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Reaction-diffusion operator Green’s function surrogate model deep learning fast solver.
Author Details
Junqing Jia Email
Lili Ju Email
Xiaoping Zhang Email