https://doi.org/10.1140/epjs/s11734-024-01263-7
Regular Article
Physical informed memory networks based on domain decomposition for solving nonlinear partial differential equations
College of Mathematics and Systems Science, Shandong University of Science and Technology, 266590, Qingdao, China
Received:
19
March
2024
Accepted:
18
July
2024
Published online:
29
July
2024
In recent years, deep learning models have emerged as a popular numerical method for solving nonlinear partial differential equations (PDEs). In this paper, the improved physical informed memory networks (PIMNs) are introduced, which are constructed upon domain decomposition. In the improved PIMNs, the solution domain is decomposed into non-overlapping rectangular sub-domains. The loss for each sub-domain is computed independently, and an adaptive function is employed to dynamically adjust the coefficients of the loss terms. This approach significantly improves the PIMNs’ ability to train regions with high loss values. To validate the superiority of the improved PIMNs, the nonlinear Schrödinger equation, the KdV-Burgers equation, and the KdV-Burgers-Kuramoto equation are solved via both the original and the improved PIMNs. The experimental results clearly show that the improved PIMNs provide a significant enhancement in terms of solution accuracy compared to the original PIMNs.
Jiuyun Sun, Huanhe Dong, Mingshuo Liu and Yong Fang have contributed equally to this work.
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