Introduction

The code is used to implement physics-driven model (PDM) and can be divided into three parts: data generation, model training, and model prediction.

Data generation

We generate the conductivity structures using Gaussian random field (GRF), and compute the MT responses by finite difference method (FDM).

There are two files for generating conductivity structuress in uniform and non-uniform grids, respectively.

• non_grid-64-ray.ipynb generates dataset in non-uniform grid. The main parameters in the code are located in the second cell. You need to modify two parameters at least, the number of samples n_sample and the file name file_name. It is important to note that the saved training data and test data should be set with different file names.

• grid-64-ray.ipynb generates dataset in uniform grid.

In addition, there are two library files, gaussian_random_fields.py is the modules of GRF, and MT2D_secondary_direct.py is the code for 2-D MT forwad modeling.

Model training

directory TE and TM are used for xy- and yx-modes, respectively. The architecture of these two directorys is the same, so let's use TE as an example to illustrate.

• run: containing excutable python files

  • conv_TM.py is the main program for predicting Hx
  • conv_TM_MSE.py uses the mean square error (MSE) as loss function
  • conv_TM_TFM.py uses the TFM as governing equation
  • conv_TM_SFM.py uses the secondary field as output
  • config.yml is a configuration file written in yaml format. For the meaning of each parameter, refer to the comment on the corresponding line.

• utils: some auxiliary python files

  • FNO.py is the Fourier Neural Operator(Li et al., 2021)
  • load_data.py is used to load and normalize the input data
  • derivative.py computes the derivatives using finite difference.

• model: saving trained model file (.pkl). (If the directory does not exist, you need to create it manually)

• Log: saving log file. (If the directory does not exist, you need to create it manually)

• temp: if stoping program early, you can find model file (.pkl) here. (If the directory does not exist, you need to create it manually)

Model prediction

copy the saved models in TE/run/model and TM/run/model to the directory eval/model after the training is completed. Then run the non_grid_plot.ipynb to plot the predicted results.

Usage

data genetation

First, create the subdirectory data under the directory Data. Second, Choose one of following two methods to generate conductivity sturctures and corresponding apparent resistivity and phase.

1. download data from from Google Cloud Drive in https://drive.google.com/drive/directorys/1RvBw3HU-hTbr6mWkF6qTyqscGDvM6FRH?usp=sharing.

or

2. generate data locally: run grid-64-ray.ipynb or non-grid-64-ray.ipynb twice in Jupyter (each time you need to modify the parameter file_name) to consturct training dataset and test dataset.

Finally, check if there is .mat file under the directory data.

model training

for xy-mode,

cd ./TE/run
# the last input is the item name in the config.yml
python conv_TE.py grid_5000

for yx-mode,

cd ./TM/run
# the last input is the item name in the config.yml
python conv_TM.py grid_5000

model prediction (plot results)

1. change directory to eval and make new subdirectory model.
2. copy the saved model files from TE/run/model and TM/run/model to the directory eval/model
3. run the non_grid_plot.ipynb in Jupyter.

Requirements

• PyTorch >=1.8.0. Pytorch 1.8.0 starts to support complex numbers and it has a new implementation of FFT

• torchinfo

• ray

• numpy

• scipy

• matplotlib

Citing

@article{peng2023rapid,
  title={Rapid surrogate modeling of magnetotelluric in the frequency domain using physics-driven deep neural networks},
  author={Peng, Zhong and Yang, Bo and Liu, Lian and Xu, Yixian},
  journal={Computers \& Geosciences},
  volume={176},
  pages={105360},
  year={2023},
  publisher={Elsevier}
}