This supplementary folder contains sample codes to generate the data used in the 
paper " Can Minkowki tensors of a porous microstructure characterize its
permeability."

Gerenation of shapes:

The random shapes used for obstacles in the porous media can be generated using 
the Jupyter notebook file, generate_shapes.ipynb. To use this notebook, the 
'shapes.py' file should be present in the same directory. 

Flow simulations: 

The simulations of flows around the obstacles can be run using the notebook file
'cfdsimulate.ipynb'. To use this notebook, the finite volume solver called 
Gerris needs to be installed in the system. 

Computing permeabilities:

The flow data can then be used to compute the permeability of each of the porous
media by fitting a polynomial on the superficial velocity. This can be achieved
by using the notebook 'compute_permeabilities.ipynb.'

Training the Deep neural network:

The data set used in the paper, generated using the functions mentioned above 
are consolidated in the folder m1, m2 and m3. The Deep Neural Network training 
can be performed on this data using the notebook file 'K_fit.ipynb'. All the 
hyperparameters used for the neural network training can be set here. The 
folders m1, m2 and m3 contain the shape information and the corresponding 
permeability values.