# Predicting bulk moduli with matminer

## Fit data mining models to ~6000 calculated bulk moduli from Materials Project

Time to complete: 30 minutes

This notebook is an example of using the MP data retrieval tool `retrieve_MP.py` to retrieve computed bulk moduli from the materials project databases in the form of a pandas dataframe, using matminer’s tools to populate the dataframe with descriptors/features from pymatgen, and then fitting regression models from the scikit-learn library to the dataset.

### Preamble

Import libraries, and set pandas display options.

    # filter warnings messages from the notebook
    import warnings
    warnings.filterwarnings('ignore')

    import numpy as np
    import pandas as pd

    # Set pandas view options
    pd.set_option('display.width', 1000)
    pd.set_option('display.max_columns', None)
    pd.set_option('display.max_rows', None)

### Step 1: Use matminer to obtain data from MP (automatically) in a “pandas” dataframe

Step 1a: Import matminer’s MP data retrieval tool and get calculated bulk moduli and possible descriptors.

    from matminer.data_retrieval.retrieve_MP import MPDataRetrieval

    api_key = None   # Set your MP API key here. If set as an environment variable 'MAPI_KEY', set it to 'None'
    mpr = MPDataRetrieval(api_key)     # Create an adapter to the MP Database.

    # criteria is to get all entries with elasticity (K_VRH is bulk modulus) data
    criteria = {'elasticity.K_VRH': {'$ne': None}}

    # properties are the materials attributes we want
    # See https://github.com/materialsproject/mapidoc for available properties you can specify
    properties = ['pretty_formula', 'spacegroup.symbol', 'elasticity.K_VRH', 'formation_energy_per_atom', 'band_gap',
                  'e_above_hull', 'density', 'volume', 'nsites']

    # get the data!
    df_mp = mpr.get_dataframe(criteria=criteria, properties=properties)
    print 'Number of bulk moduli extracted = {}'.format(len(df_mp))

`Number of bulk moduli extracted = 6023`

Step 1b: Explore the dataset.

    df_mp.head()
    df_mp.describe()

Step 1c. Filter out unstable entries and negative bulk moduli

    df_mp = df_mp[df_mp['elasticity.K_VRH'] > 0]
    df_mp = df_mp[df_mp['e_above_hull'] < 0.1]
    df_mp.describe()

### Step 2: Add descriptors/features

Step 2a: create volume per atom descriptor

    # add volume per atom descriptor
    df_mp['vpa'] = df_mp['volume']/df_mp['nsites']

    # explore columns
    df_mp.head()

Step 2b: add several more descriptors using MatMiner’s pymatgen descriptor getter tools

    from matminer.featurizers.composition import ElementProperty
    from matminer.featurizers.data import PymatgenData
    from pymatgen import Composition

    df_mp["composition"] = df_mp['pretty_formula'].map(lambda x: Composition(x))

    dataset = PymatgenData()
    descriptors = ['row', 'group', 'atomic_mass',
                   'atomic_radius', 'boiling_point', 'melting_point', 'X']
    stats = ["mean", "std_dev"]

    ep = ElementProperty(data_source=dataset, features=descriptors, stats=stats)
    df_mp = ep.featurize_dataframe(df_mp, "composition")

    #Remove NaN values
    df_mp = df_mp.dropna()

    df_mp.head()

### Step 3: Fit a Linear Regression model, get R2 and RMSE

Step 3a: Define what column is the target output, and what are the relevant descriptors

    # target output column
    y = df_mp['elasticity.K_VRH'].values

    # possible descriptor columns
    X_cols = [c for c in df_mp.columns
              if c not in ['elasticity.K_VRH', 'pretty_formula',
                           'volume', 'nsites', 'spacegroup.symbol', 'e_above_hull', 'composition']]
    X = df_mp.as_matrix(X_cols)

    print("Possible descriptors are: {}".format(X_cols))

    Possible descriptors are: ['formation_energy_per_atom', 'band_gap', 'density', 'vpa', 'mean X', 'mean atomic_mass',
    'mean atomic_radius', 'mean boiling_point', 'mean group', 'mean melting_point', 'mean row', 'std_dev X',
    'std_dev atomic_mass', 'std_dev atomic_radius', 'std_dev boiling_point', 'std_dev group', 'std_dev melting_point',
    'std_dev row']

Step 3b: Fit the linear regression model

    from sklearn.linear_model import LinearRegression
    from sklearn.metrics import mean_squared_error

    lr = LinearRegression()

    lr.fit(X, y)

    # get fit statistics
    print 'R2 = ' + str(round(lr.score(X, y), 3))
    print 'RMSE = %.3f' % np.sqrt(mean_squared_error(y_true=y, y_pred=lr.predict(X)))

    R2 = 0.804
    RMSE = 32.558

Step 3c: Cross validate the results

    from sklearn.model_selection import KFold, cross_val_score

    # Use 10-fold cross validation (90% training, 10% test)
    crossvalidation = KFold(n_splits=10, shuffle=True, random_state=1)

    # compute cross validation scores for random forest model
    scores = cross_val_score(lr, X, y, scoring='mean_squared_error',
                             cv=crossvalidation, n_jobs=1)
    rmse_scores = [np.sqrt(abs(s)) for s in scores]

    print 'Cross-validation results:'
    print 'Folds: %i, mean RMSE: %.3f' % (len(scores), np.mean(np.abs(rmse_scores)))

    Cross-validation results:
    Folds: 10, mean RMSE: 33.200

### Step 4: Plot the results with FigRecipes

    from matminer.figrecipes.plotly.make_plots import PlotlyFig

    pf = PlotlyFig(x_title='DFT (MP) bulk modulus (GPa)',
                   y_title='Predicted bulk modulus (GPa)',
                   plot_title='Linear regression',
                   plot_mode='offline',
                   margin_left=150,
                   textsize=35,
                   ticksize=30,
                   filename="lr_regression.html")

    # a line to represent a perfect model with 1:1 prediction
    xy_params = {'x_col': [0, 400],
                 'y_col': [0, 400],
                 'color': 'black',
                 'mode': 'lines',
                 'legend': None,
                 'text': None,
                 'size': None}

    pf.xy_plot(x_col=y,
               y_col=lr.predict(X),
               size=3,
               marker_outline_width=0.5,
               text=df_mp['pretty_formula'],
               add_xy_plot=[xy_params])

Great! We just fit a linear regression model to pymatgen features using matminer and sklearn. Now let’s use a Random Forest model to examine the importance of our features.

### Step 5: Follow similar steps for a Random Forest model

Step 5a: Fit the Random Forest model, get R2 and RMSE

    from sklearn.ensemble import RandomForestRegressor

    rf = RandomForestRegressor(n_estimators=50, random_state=1)

    rf.fit(X, y)
    print 'R2 = ' + str(round(rf.score(X, y), 3))
    print 'RMSE = %.3f' % np.sqrt(mean_squared_error(y_true=y, y_pred=rf.predict(X)))

    R2 = 0.988
    RMSE = 7.947

Step 5b: Cross-validate the results

    # compute cross validation scores for random forest model
    scores = cross_val_score(rf, X, y, scoring='mean_squared_error', cv=crossvalidation, n_jobs=1)

    rmse_scores = [np.sqrt(abs(s)) for s in scores]
    print 'Cross-validation results:'
    print 'Folds: %i, mean RMSE: %.3f' % (len(scores), np.mean(np.abs(rmse_scores)))

    Cross-validation results:
    Folds: 10, mean RMSE: 20.087

### Step 6: Plot our results and determine what features are the most important

Step 6a: Plot the random forest model

    from matminer.figrecipes.plotly.make_plots import PlotlyFig

    pf_rf = PlotlyFig(x_title='DFT (MP) bulk modulus (GPa)',
                      y_title='Random forest bulk modulus (GPa)',
                      plot_title='Random forest regression',
                      plot_mode='offline',
                      margin_left=150,
                      textsize=35,
                      ticksize=30,
                      filename="rf_regression.html")

    # a line to represent a perfect model with 1:1 prediction
    xy_line = {'x_col': [0, 450],
               'y_col': [0, 450],
               'color': 'black',
               'mode': 'lines',
               'legend': None,
               'text': None,
               'size': None}

    pf_rf.xy_plot(x_col=y,
                  y_col=rf.predict(X),
                  size=3,
                  marker_outline_width=0.5,
                  text=df_mp['pretty_formula'],
                  add_xy_plot=[xy_line])

Step 6b: Plot the importance of the features we used

    importances = rf.feature_importances_
    X_cols = np.asarray(X_cols)
    indices = np.argsort(importances)[::-1]

    pf = PlotlyFig(y_title='Importance (%)',
                   plot_title='Feature by importances',
                   plot_mode='offline',
                   margin_left=150,
                   margin_bottom=200,
                   textsize=20,
                   ticksize=15,
                   filename="rf_importances.html")

    pf.bar_chart(x=X_cols[indices], y=importances[indices])