This repository reproduces the results of the submitted paper "A versatile framework to solve the Helmholtz equation using physics-informed neural networks." to Geophysical Journal International.
We applied the physics-informed neural networks (PINNs) to solve the Helmholtz equation for isotropic and anisotropic media. The proposed method has resilience and versatility in predicting frequency-domain wavefields for different media and model shapes.
CPU usage: pip install --pre "tensorflow==1.15.*"
GPU usage: pip install --pre "tensorflow-gpu==1.15.*"
Helm_pinn_tanh.py: Solving the Helmholtz equation using PINN with tanh activation function for isotropic media
Helm_pinn_sine_adaptive.py: Solving the Helmholtz equation using PINN with adpative sine activation function for isotropic media
Helm_pinn_sine_fixed.py: Solving the Helmholtz equation using PINN with fixed sine activation function for isotropic media
Helm_pinn_sine_vti_adaptive.py: Solving the Helmholtz equation using PINN with fixed sine activation function for VTI media
Helm_pinn_ps_sine_tti_topo.py: Solving the Helmholtz equation using PINN with fixed sine activation function for TTI media
Part of Matlab codes are included in my other repository
If you find our codes and publications helpful, please kindly cite the following publication.
@article{song2022versatile, title={A versatile framework to solve the Helmholtz equation using physics-informed neural networks}, author={Song, Chao and Alkhalifah, Tariq and Waheed, Umair Bin}, journal={Geophysical Journal International}, volume={228}, number={3}, pages={1750--1762}, year={2022}, publisher={Oxford University Press} }
If there are any problems, please contact me through my emails: chao.song@kaust.edu.sa;csong1@ic.ac.uk