Elastic net

Machine learning model for predicting multi-component transition metal carbides (MTMCs)

This is the manual to reproduce results and support conclusions of Lattice Distortion Informed Exceptional Multi-Component Transition Metal Carbides Discovered by Machine Learning.

We recommend using a Linux/Windows operating system to run the following examples, under the current directory.

Table of Contents

• Installation

• Example of using the well-trained model

• Train a new model from scratch

  • Prepare DFT calculations
  • Collect DFT results
  • Run main function
  • Collect input features and labels
  • Train
  • Check training results
  • Predict
  • High-throughput predict
  • Ternary plot

• Other scripts

  • Get ROM
  • get VEC

• Abbreviations

Installation

Install under conda environment

• Create a new environment

conda create -n ElasticNet python==3.10

• Activate the environment

conda activate ElasticNet

• Install package

pip install elasticnet

Alternatively, you can install with pip.

• Install the package. Use --user option if you don't have the root permission.

pip install elasticnet --user

• If your IP locates in mainland China, you may need to install it from the tsinghua mirror.

pip install elasticnet -i https://pypi.tuna.tsinghua.edu.cn/simple

Requirements file: requirements.txt

Key modules

numpy==1.25.0    
scikit-learn==1.2.2   
tensorflow==2.10.0   
ase==3.22.1  
pandas==1.5.3

Example of using the well-trained model

• Download the well-trained parameters: checkpoint
• Run the following python code:

from elasticnet import predict_formula  
pf = predict_formula(config='input_config.json',ckpt_file='checkpoint')  
pf.predict(*['VNbTa', 'TiNbTa'])  

• The mechanical properties of (VNbTa)C3 and (TiNbTa)C3 will show on the screen. The specific modulus of each column is: B, G, E, Hv, C11, C44.

array([[294.43195 , 203.70157 , 496.67032 ,  25.989697, 632.3356  ,
        175.50716 ],
       [283.17245 , 201.96506 , 489.7816  ,  26.824062, 607.07336 ,
        178.52579 ]], dtype=float32)

Train a new model from scratch

Prepare DFT calculations

• Bulk optimization.
• Elastic constants calculation.

Collect DFT results

• Collect elastic constants into a file with csv extension. See example: files/HECC_properties_over_sample.CSV.
• You may refer to these papers to calculate modulus from C11, C12, and C44: PHYSICAL REVIEW B 87, 094114 (2013) and Journal of the European Ceramic Society 41 (2021) 6267-6274
• The *csv file should contain at least these columns: nominal_formula, C11, C12, C44, B, G, E, Hv, and real_formula. See example: files/HECC_properties_over_sample.CSV.

Prepare configurations files

• input_config.json: defines how to generate input features and labels. You are recommended to download this file and modify then.

  Variable	Type	Meaning
  include_more	bool	If True, the bulk_energy_per_formula and volume_per_formula are also be included in the input features.
  split_test	bool	If True, a new test set will be split from the dataset. For cross validation, it is OK to set this as False.
  clean_by_pearson_r	bool	Clean input features. Highly correlated features will be removed if this is True.
  reduce_dimension_by_pca	bool	Clean input features by PCA. Choose one among clean_by_pearson_r and reduce_dimension_by_pca.
  prop_precursor_path	str	A file storing the properties of precursory binary carbides. File extension can be *.csv and *.json. See example: file/HECC_precursors.csv
  model_save_path	str	Path for storing PCA model and other information when generating input features and labels
  props	list	A list of properties that are encoded into the input features. Choose among the column names of files/HECC_precursors.csv.
  operators	list	A list of operators to expand the input dimension. Choose among: ['cube', 'exp_n', 'exp', 'plus', 'minus', 'multiply', 'sqrt', 'log10', 'log', 'square'].
  HECC_properties_path	str	A file contains the collected properties of MTMCs.
  labels	list	A list of label names that need to fit/learn.
  soap_features	bool	Whether to use SOAP descriptor.
  soap_config	dict	A python dict that defines the configuration of SOAP descriptor. - input_structure_type: 'POSCAR' or 'CONTCAR'. Use 'POSCAR' or 'CONTCAR' to generate SOAP features. - You can find the explanations for other specifications here: SOAP.__init__

• train.json: defines how to train the machine-learning model.

  Variable	Type	Meaning
  Nodes_per_layer	list	Number of nodes of every hidden layers
  Number_of_fold	int	Number of cross-validation folds. Normally 5 or 10.
  feature_file	str	A file contains input features.
  label_file	str	A file contains labels of samples.
  Activation_function	str	Activation function of hidden layers. Alternatives: 'relu', 'softmax', 'sigmoid', 'tanh'
  Output_activation	str	Activation function of the output layer. Alternatives: 'relu', 'softmax', 'sigmoid', 'tanh'
  Number_of_out_node	int/'auto'	Number of nodes of the output layer. If there is only one column in the label_file, this variable should be 1. 'auto' is for multiple columns.
  Optimizer	str	The name of the optimizer. Examples: tf.keras.optimizers
  Cost_function	str	Name of cost function in Tensorflow. Examples: tf.keras.losses
  Metrics	list	A list of metrics to evaluate the model. Examples: tf.keras.metrics
  Batch_size	int	The batch size. See tf.keras.Model.fit
  Epochs	int	Number of epochs for training. See tf.keras.Model.fit
  Verbose	int	Verbosity mode. See tf.keras.Model.fit
  Regularization	bool	Whether to used the L2 regularization. See tf.keras.regularizers.L2.
  Model_save_path	str	A folder to store the well-trained NN model.
  Log_save_path	str	A folder to store the training log.
  Prediction_save_path	str	A folder to store the predictions of input features after training.
  SEED	int	Random seed for shuffling input dataset.

Run main function

python -m elasticnet

The following python code will be executed.

def main():
    # prepare dataset
    from elasticnet.prepare_input import x_main, y_main
    x_main('input_config.json', load_PCA=False, save_PCA=True)
    y_main('input_config.json')

    # train
    from elasticnet.ann import CV_ML_RUN, load_and_pred
    CV_ML_RUN('train.json')
    load_and_pred('train.json', 'x_data_after_pca.txt', write_pred_log=True, drop_cols=None)

main()

You may want to prepare the dataset and train the model in separate steps, see below ↓.

Collect input features and labels

from elasticnet.prepare_input import x_main, y_main
x_main('input_config.json', load_PCA=False, save_PCA=True)
y_main('input_config.json')

Three files will be generated:

• x_data_init.txt: input features without PCA.
• x_data_after_pca.txt: input features after PCA.
• y_data.txt: labels

Train

• Run the following python code.

from elasticnet import CV_ML_RUN, load_and_pred
if __name__ == '__main__':
    CV_ML_RUN('train.json')
    load_and_pred('train.json', 'x_data_after_pca.txt', write_pred_log=True, drop_cols=None)

• You can also execute python -m elasticnet directly in the console. See Run main function.

Check training results

• Generated files/folders
  • checkpoint: A folder for PCA model, NN model, and other information for generating input features.
    • cp.ckpt: Location of NN model.
    • log: Learning curves and weights of all CV models.
      • The file with extension *.global.acc.loss summarizes the model performance. Example: 4_layer-80_80_80_80_nodes.global.acc.loss
    • pred: Predictions of input features.
      • prediction_all.txt: all CV models.
      • prediction_mean.txt: average of CV models.
    • pca_model.joblib: PCA model.
    • scale_range.json: Range to rescale input features.
    • scale_range_1.json: Range to rescale input features again.

Predict

• After training, run the following python code:

from elasticnet import predict_formula  
pf = predict_formula(config='input_config.json',ckpt_file='checkpoint')  
pf.predict(*['VNbTa', 'TiNbTa'])   

• The mechanical properties of (VNbTa)C3 and (TiNbTa)C3 will show on the screen. The specific modulus of each column is: B, G, E, Hv, C11, C44.

array([[294.43195 , 203.70157 , 496.67032 ,  25.989697, 632.3356  ,
        175.50716 ],
       [283.17245 , 201.96506 , 489.7816  ,  26.824062, 607.07336 ,
        178.52579 ]], dtype=float32)

High-throughput predict

• Run the following python code:

from elasticnet import high_throughput_predict
high_throughput_predict() 

• Output: ANN_predictions.xlsx

Ternary plot

• Run the following python code:

from elasticnet import ternary_plot
ternary_plot(elements = ['Ti', 'Nb', 'Ta'])

• Alternatively, elements = ['VNbTa', 'Ti', 'Hf'].

• Output: phase_diagrams/**_diagram.csv

• Plot.

Other scripts

Get ROM

• Run the following python code:

from elasticnet import get_rom
ROM = get_rom(config='input_config.json', formulas='formulas.txt', props=['B', 'G', 'E', 'Hv', 'VEC'])
print(ROM)

• Output. If the formulas.txt contains ['VNbTa', 'TiNbTa'] only.

array([[310.33922223, 210.80075867, 515.61666613,  26.20022487,
          9.        ],
       [291.74733333, 199.9075404 , 488.11937417,  25.52194014,
          8.66666667]])

Get VEC

• VEC is simply the last column of Get ROM.

Abbreviations

Abbr.	Full name
MTMC	Multi-component transition metal carbides
HECC	High-entropy carbide ceramic
HEC	High-entropy ceramic
ML	Machine learning
SOAP	Smooth overlap of atomic positions
NN	Neural networks
CV	cross validation
ROM	Rule of mixtures
VEC	Valence electron concentration