Newton’s Method and Its Hybrid with Machine Learning for Navier-Stokes Darcy Models Discretized by Mixed Element Methods
Year: 2025
Author: Jianguo Huang, Hui Peng, Haohao Wu
Communications in Computational Physics, Vol. 37 (2025), Iss. 1 : pp. 30–60
Abstract
This paper focuses on discussing Newton’s method and its hybrid with machine learning for the steady state Navier-Stokes Darcy model discretized by mixed element methods. First, a Newton iterative method is introduced for solving the relative discretized problem. It is proved technically that this method converges quadratically with the convergence rate independent of the mixed element mesh size, under certain standard conditions. Later on, a deep learning algorithm is proposed for solving this nonlinear coupled problem. Following the ideas of an earlier work by Huang, Wang and Yang (2020), an Int-Deep algorithm is constructed by combining the previous two methods so as to further improve the computational efficiency and robustness. A series of numerical examples are reported to show the numerical performance of the proposed methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2024-0066
Communications in Computational Physics, Vol. 37 (2025), Iss. 1 : pp. 30–60
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Navier Stokes-Darcy model deep learning Newton iterative method Int-Deep method convergence analysis. Navier-Stokes Darcy model