@Article{IJNAM-21-697,
author = {Jia , JunqingJu , Lili and Zhang , Xiaoping},
title = {Deep Surrogate Model for Learning Green’s Function Associated with Linear Reaction-Diffusion Operator },
journal = {International Journal of Numerical Analysis and Modeling},
year = {2024},
volume = {21},
number = {5},
pages = {697--715},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2024-1028},
url = {http://global-sci.org/intro/article_detail/ijnam/23449.html}
}