RCNN: Recurrent Convolutional Neural Network for Solving 3-D Wave Equation

The solution of the 3D wave equation holds significant importance in various fields, but traditional numerical methods employed for solving this equation are typically time-consuming. Recently, machine learning-based methods have gained popularity for solving wave equations owing to their capacity to predict physical phenomena. Nonetheless, current research is limited to solving 1D and 2D wave equations due to the complex nature of the solutions of the 3D wave equation. Therefore, a recurrent convolutional neural network (RCNN) that leverages the similarity between RNN and the time-marching process, and the consistency of convolutional layers (CLs) with spatial differentiation, is proposed to solve 3D wave equation. Taking advantage of the latest advances in machine learning framework, RCNN makes it unsophisticated to achieve efficient GPU computing. Numerical examples demonstrate that the RCNN achieves considerable accuracy and impressive computational efficiency in solving the 3D wave equation.