A conservative hybrid physics-informed neural network method for
Maxwell-Amp\`{e}re-Nernst-Planck equations
- URL: http://arxiv.org/abs/2312.05891v1
- Date: Sun, 10 Dec 2023 13:58:41 GMT
- Title: A conservative hybrid physics-informed neural network method for
Maxwell-Amp\`{e}re-Nernst-Planck equations
- Authors: Cheng Chang, Zhouping Xin, Tieyong Zeng
- Abstract summary: The proposed hybrid algorithm provides an automated means to determine a proper approximation for dummy variables.
The original method is validated for 2-dimensional problems.
The proposed method can be readily generalised to cases with one spatial dimension.
- Score: 22.81295238376119
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Maxwell-Amp\`{e}re-Nernst-Planck (MANP) equations were recently proposed to
model the dynamics of charged particles. In this study, we enhance a numerical
algorithm of this system with deep learning tools. The proposed hybrid
algorithm provides an automated means to determine a proper approximation for
the dummy variables, which can otherwise only be obtained through massive
numerical tests. In addition, the original method is validated for
2-dimensional problems. However, when the spatial dimension is one, the
original curl-free relaxation component is inapplicable, and the approximation
formula for dummy variables, which works well in a 2-dimensional scenario,
fails to provide a reasonable output in the 1-dimensional case. The proposed
method can be readily generalised to cases with one spatial dimension.
Experiments show numerical stability and good convergence to the steady-state
solution obtained from Poisson-Boltzmann type equations in the 1-dimensional
case. The experiments conducted in the 2-dimensional case indicate that the
proposed method preserves the conservation properties.
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