An Efficient Platform for Numerical Modeling of Partial Differential Equations

Solving partial differential equations (PDEs) is a fundamental task for computational electromagnetic and mechanical wave modeling, which hold utmost significance in remote sensing and geophysics. The importance of efficient PDEs solving methods lies in their ability to provide rapid simulations and...

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Bibliographic Details
Published in:IEEE transactions on geoscience and remote sensing 2024, Vol.62, p.1-13
Main Authors: Ji, Duofa, Li, Chenxi, Zhai, Changhai, Cao, Zelin
Format: Article
Language:English
Subjects:
Acoustic waves
Artificial neural networks
Deep learning
Differential equations
Efficiency
Efficient numerical modeling
Geophysical methods
Geophysics
Machine learning
machine learning framework
Magnetic fields
Mathematical models
Modelling
Neural networks
Numerical methods
Numerical models
P-waves
Partial differential equations
partial differential equations (PDEs)
Real time
recurrent convolutional neural network (RCNN)
Recurrent neural networks
Remote sensing
Seismic waves
Spatial discrimination learning
Three-dimensional displays
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Summary:Solving partial differential equations (PDEs) is a fundamental task for computational electromagnetic and mechanical wave modeling, which hold utmost significance in remote sensing and geophysics. The importance of efficient PDEs solving methods lies in their ability to provide rapid simulations and real-time predictions. However, as the scale and dimensionality of the problems increase, the efficiency of current numerical methods becomes a concern. Therefore, this study leverages the inherent connection between the temporal-spatial stepping processes and recurrent neural networks (RNNs) as well as convolutional layers (CLs) to propose a general-purpose recurrent convolutional neural network (RCNN) platform for solving PDEs. The RCNN platform rigorously executes the temporal-spatial iterations involved in discretized forms of PDEs. Furthermore, benefiting from the latest advancements in deep learning, the platform enhances the efficiency of convolutional computations. By applying the RCNN platform to electromagnetic, acoustic wave, and seismic wave modeling, among others, its reliability and high efficiency in solving various high-dimensional PDEs are demonstrated.
ISSN:0196-2892
1558-0644
DOI:10.1109/TGRS.2024.3409620