Extended Particle Weak-Form-Based Neural Networks for Seismic Modeling

The simulation of seismic wave propagation through the solution of wave equations is considered one of the fundamental topics in applied geophysics. Physics-informed neural networks (PINNs) have been widely used in geophysics as an alternative to traditional numerical methods for solving wave equations. In this work, we introduce a novel deep-learning-based framework named particle weak-form-based neural networks (ParticleWNN) to achieve better wavefield solutions in seismic modeling. The ParticleWNN is developed for solving partial differential equations (PDEs) in the weak form where the trial space is the space of deep neural networks (DNNs) and the test space is constructed by functions compactly supported in small regions. Compared with vanilla PINN, ParticleWNN offers several advantages, such as requiring less regularity, allowing local training, and parallel implementation via domain decomposition. The efficiency and accuracy of the proposed method in simulating seismic wave propagation are demonstrated by several numerical examples.