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PINN-Helmholtz-solver-adaptive-sine

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.

Overview

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.

Installation of Tensorflow1

CPU usage: pip install --pre "tensorflow==1.15.*"

GPU usage: pip install --pre "tensorflow-gpu==1.15.*"

Code explanation

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

Citation information

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}
}

contact information

If there are any problems, please contact me through my emails: [email protected];[email protected]