This repository holds the code for the paper "Learning crystal field parameters using convolutional neural networks" authored by Noah F. Berthusen, Yuriy Sizyuk, Mathias S. Scheurer, and Peter P. Orth. This work presents a deep machine learning algorithm that uses a two-dimensional convolutional neural network (CNN) to determine crystal field Stevens parameters from thermodynamic observables, given a total angular momentum J of the ground state multiplet and crystal field site symmetry group G.

This document will guide you through installing and running the code.

The network can be trained to predict the Stevens parameters for a given point group symmetry. Training the network to predict the coefficients for experimental examples can also be done. For both, a sizeable amount of training data needs to be generated.

1. Download repository and update your python environment.

   • If you are familiar with git, clone the repository with the following command:

     git clone [email protected]:Orth-Research/ml_cr.git
     

     Alternatively, on the top right page of this page, download the zipped version of the repository and unpack at your desired place.

2. Prepare your data

   • Specify all of the required data in DataGeneration.py. This includes temperature and magnetic field ranges for specific heat, susceptibility, and magnetization, magnetic field lattice directions, and of course the point group symmetry G and the angular momentum quantum numbers J (total angular momentum), L (total orbital angular momentum), and S (total spin) of the ground state multiplet. The program can be run entirely with command line arguments. View the command line arguments with the following command

     python DataGeneration.py -h
     

     The required variables could also be hard-coded from within the program if working with the command line arguments is cumbersome. The output directory can be specified, and the data will be saved as OUTPUT_DIR/generated_data.csv, and the target Stevens parameters will be saved as OUTPUT_DIR/generated_targets.csv.
   • Generate training data in amounts suitable to be trained on.
   • Using command line arguments, specify the input and output directories for WaveletTransform.py to transform the 1D thermodynamic observable data into the 2D scaleogram format that is needed for the CNN architecture. The program expects the input data to have the filename INPUT_DIR/generated_data.csv. In this file, you can choose to save the mean and standard deviations for the generated_data/targets. This is needed while training and when evaluating any predictions after training.

3. Train model

   • The following is best done on a GPU device. After specifying the location of CWT data generated in step 2 through command line arguments, run StevensTraining.py to train the CNN. Specify training, validation, and out directories to load the training/validation data, and to save the trained model. The number of epochs, batch size, and early stopping threshold can also be specified.