An Efficient Platform for Numerical Modeling of Partial Differential Equations

• 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
• ISSN: 0196-2892; 1558-0644
• DOI: 10.1109/TGRS.2024.3409620

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.