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
If you find our codes and publications helpful, please kindly cite the following publication.
@article{song2021versatile,
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={},
number={},
pages={},
year={2021},
publisher={Oxford University Press}
}
If there are any problems, please contact me through my emails: chao.song@kaust.edu.sa;csong1@ic.ac.uk