Year: 2024
Author: Xiaofei Guan, Boya Hu, Shipeng Mao, Xintong Wang, Zihao Yang
Communications in Computational Physics, Vol. 36 (2024), Iss. 4 : pp. 943–976
Abstract
Designing efficient and high-accuracy numerical methods for complex dynamic incompressible Magnetohydrodynamics (MHD) equations remains a challenging problem in various analysis and design tasks. This is mainly due to the nonlinear coupling of the magnetic and velocity fields occurring with convection and Lorentz forces, and multiple physical constraints, which will lead to the limitations of numerical computation. In this paper, we develop the MHDnet as a physics-preserving learning approach to solve MHD problems, where three different mathematical formulations are considered and named $B$ formulation, $A_1$ formulation, and $A_2$ formulation. Then the formulations are embedded into the MHDnet that can preserve the underlying physical properties and divergence-free condition. Moreover, MHDnet is designed by the multi-modes feature merging with multiscale neural network architecture, which can accelerate the convergence of the neural networks (NN) by alleviating the interaction of magnetic fluid coupling across different frequency modes. Furthermore, the pressure fields of three formulations, as the hidden state, can be obtained without extra data and computational cost. Several numerical experiments are presented to demonstrate the performance of the proposed MHDnet compared with different NN architectures and numerical formulations. In future work, we will develop possible applications of inverse problems for coupled equation systems based on the framework proposed in this paper.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2024-0002
Communications in Computational Physics, Vol. 36 (2024), Iss. 4 : pp. 943–976
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Magnetohydrodynamics multiscale neural network physics-preserving formulation divergence-free multi-modes feature.