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
  console conda create -n ElasticNet python==3.10

• Activate the environment
  console conda activate ElasticNet

• Install package
  console pip install elasticnet

Alternatively, you can install with pip.

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

• If your IP locates in mainland China, you may need to install it from the tsinghua mirror.
  console 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:
  python 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. python 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/HECCpropertiesover_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/HECCpropertiesover_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 |
  | -------------------- | ---- | ------------------------------------------------------------------------------------------------------------ |
  | includemore | bool | If True, the `bulkenergyperformulaandvolumeperformulaare also be included in the input features. | | split_test | bool | IfTrue, a new test set will be split from the dataset. For cross validation, it is OK to set this asFalse. | | clean_by_pearson_r | bool | Clean input features. Highly correlated features will be removed if this isTrue. | | reduce_dimension_by_pca | bool | Clean input features by [PCA](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html#sklearn-decomposition-pca). Choose one amongcleanbypearsonrandreducedimensionbypca. | | prop_precursor_path | str | A file storing the properties of precursory binary carbides. File extension can be.csvand.json. See example: [file/HECC_precursors.csv](file/HECC_precursors.csv)| | model_save_path | str | Path for storing [PCA](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html#sklearn-decomposition-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](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](https://singroup.github.io/dscribe/latest/tutorials/descriptors/soap.html) descriptor. | | soap_config | dict | A python dict that defines the configuration of [SOAP](https://singroup.github.io/dscribe/latest/tutorials/descriptors/soap.html) descriptor. - input_structure_type: 'POSCAR' or 'CONTCAR'. Use 'POSCAR' or 'CONTCAR' to generate [SOAP](https://singroup.github.io/dscribe/latest/tutorials/descriptors/soap.html) features. - You can find the explanations for other specifications here: [SOAP.init`](https://singroup.github.io/dscribe/latest/tutorials/descriptors/soap.html#dscribe.descriptors.soap.SOAP.init) |

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

| Variable | Type | Meaning |
| -------------------- | ---- | ------------------------------------------------------------------------------------------------------------ | | Nodesperlayer | list | Number of nodes of every hidden layers |
| Numberoffold | int | Number of cross-validation folds. Normally 5 or 10. |
| featurefile | str | A file contains input features. |
| labelfile | str | A file contains labels of samples. |
| Activationfunction | str | Activation function of hidden layers. Alternatives: 'relu', 'softmax', 'sigmoid', 'tanh' |
| Outputactivation | str | Activation function of the output layer. Alternatives: 'relu', 'softmax', 'sigmoid', 'tanh' |
| Numberofoutnode | int/'auto' | Number of nodes of the output layer. If there is only one column in the `labelfile, this variable should be1. 'auto' is for multiple columns. | | Optimizer | str | The name of the optimizer. Examples: [tf.keras.optimizers](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers) | | Cost_function | str | Name of cost function inTensorflow. Examples: [tf.keras.losses](https://www.tensorflow.org/api_docs/python/tf/keras/losses) | | Metrics | list | A list of metrics to evaluate the model. Examples: [tf.keras.metrics](https://www.tensorflow.org/api_docs/python/tf/keras/metrics) | | Batch_size | int | The batch size. See [tf.keras.Model.fit](https://www.tensorflow.org/api_docs/python/tf/keras/Model#fit) | | Epochs | int | Number of epochs for training. See [tf.keras.Model.fit](https://www.tensorflow.org/api_docs/python/tf/keras/Model#fit) | | Verbose | int | Verbosity mode. See [tf.keras.Model.fit](https://www.tensorflow.org/api_docs/python/tf/keras/Model#fit) | | Regularization | bool | Whether to used the L2 regularization. See [tf.keras.regularizers.L2`](https://www.tensorflow.org/apidocs/python/tf/keras/regularizers/L2). | | Modelsavepath | str | A folder to store the well-trained NN model. | | Logsavepath | str | A folder to store the training log. | | Predictionsave_path | str | A folder to store the predictions of input features after training. | | SEED | int | Random seed for shuffling input dataset. |

Run main function

console python -m elasticnet

The following python code will be executed. ```python def main(): # prepare dataset from elasticnet.prepareinput import xmain, ymain xmain('inputconfig.json', loadPCA=False, savePCA=True) ymain('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

python 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.
  python 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: 4layer-80808080_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.
  • scalerange1.json: Range to rescale input features again.

Predict

• After training, run the following python code:
  python 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. python 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:
  python from elasticnet import high_throughput_predict high_throughput_predict()
• Output: ANN_predictions.xlsx

Ternary plot

• Run the following python code:
  python from elasticnet import ternary_plot ternary_plot(elements = ['Ti', 'Nb', 'Ta'])

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

• Output: phasediagrams/**diagram.csv

• Plot.

Other scripts

Get ROM

• Run the following python code:
  python 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. python 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 |