Year: 2023
Author: Yinghao Chen, Muzhou Hou, Shen Cao, Yinghao Chen, Yuntian Chen, Jinyong Ying, Shen Cao, Yuntian Chen, Jinyong Ying
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 4 : pp. 883–913
Abstract
Deep learning techniques for solving elliptic interface problems have gained significant attentions. In this paper, we introduce a hybrid residual and weak form (HRW) loss aimed at mitigating the challenge of model training. HRW utilizes the functions residual loss and Ritz method in an adversary-system, which enhances the probability of jumping out of the local optimum even when the loss landscape comprises multiple soft constraints (regularization terms), thus improving model’s capability and robustness. For the problem with interface conditions, unlike existing methods that use the domain decomposition, we design a Pre-activated ResNet of ResNet (PRoR) network structure employing a single network to feed both coordinates and corresponding subdomain indicators, thus reduces the number of parameters. The effectiveness and improvements of the PRoR with HRW are verified on two-dimensional interface problems with regular or irregular interfaces. We then apply the PRoR with HRW to solve the size-modified Poisson-Boltzmann equation, an improved dielectric continuum model for predicting the electrostatic potentials in an ionic solvent by considering the steric effects. Our findings demonstrate that the PRoR with HRW accurately approximates solvation free-energies of three proteins with irregular interfaces, showing the competitive results compared to the ones obtained using the finite element method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2023-0097
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 4 : pp. 883–913
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Deep learning method elliptic interface problem size-modified Poisson-Boltzmann equation solvation free energy
Author Details
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Improved multi-scale fusion network for solving non-smooth elliptic interface problems with applications
Ying, Jinyong
Li, Jiao
Liu, Qiong
Chen, Yinghao
Applied Mathematical Modelling, Vol. 132 (2024), Iss. P.274
https://doi.org/10.1016/j.apm.2024.04.039 [Citations: 0]