ai4materials allows to apply state-of-the-art data-analytics models to relevant materials science. Below, we present an example based on compressed sensing.
ai4materials.models.l1_l0-example
This example shows how to find descriptive parameters (short formulas) that predict crystal structure, using the example of octet binary compounds that have either rocksalt (RS) or zincblende (ZB) structure. It is based on Ref.1, and it allows to reproduce the results presented in Fig. 2 of this reference.
Starting from simple physical quantities ("building blocks", here properties of the constituent free atoms such as orbital radii), thousands of candidate formulas are generated by applying arithmetic operations combining building blocks, for example forming sums and products of them. These candidate formulas constitute the so-called "feature space". Then, a sparse regression method is used to select only a few of these formulas that explain the data.
The code below performs following steps:
- read the dataset containing binary materials from file
- calculate the atomic features using the descriptor :py
ai4materials.descriptors.atomic_features.AtomicFeatures - calculate the descriptive parameters using the LASSO+l0 method with :py
ai4materials.wrappers.calc_model - plot the results.
import sys import os.path
atomic_data_dir = os.path.normpath('/home/ziletti/nomad/nomad-lab-base/analysis-tools/atomic-data') sys.path.insert(0, atomic_data_dir)
import matplotlib.pyplot as plt from ai4materials.utils.utils_config import set_configs from ai4materials.utils.utils_config import setup_logger from ai4materials.utils.utils_data_retrieval import read_ase_db from ai4materials.wrappers import load_descriptor from ai4materials.wrappers import calc_model from ai4materials.wrappers import calc_descriptor from ai4materials.descriptors.atomic_features import AtomicFeatures from ai4materials.descriptors.atomic_features import get_table_atomic_features from ai4materials.utils.utils_config import get_data_filename from ai4materials.visualization.viewer import read_control_file import numpy as np import pandas as pd
# modify this path if you want to save the calculation results in another location configs = set_configs(main_folder='./l1_l0_example') logger = setup_logger(configs, level='INFO')
# setup folder and files lookup_file = os.path.join(configs['io']['main_folder'], 'lookup.dat') materials_map_plot_file = os.path.join(configs['io']['main_folder'], 'binaries_l1_l0_map_prl2015.png')
# define descriptor - atomic features in this case kwargs = {'energy_unit': 'eV', 'length_unit': 'angstrom'} descriptor = AtomicFeatures(configs=configs, **kwargs)
# ============================================================================= # Descriptor calculation # =============================================================================
desc_file_name = 'atomic_features_binaries' ase_db_file = get_data_filename('data/db_ase/binaries_lowest_energy_ghiringhelli2015.json') ase_atoms_list = read_ase_db(db_path=ase_db_file)
- selected_feature_list = ['atomic_ionization_potential', 'atomic_electron_affinity', 'atomic_rs_max',
'atomic_rp_max', 'atomic_rd_max']
allowed_operations = ['+', '-', '/', '', 'exp', '^2']
- desc_file_path = calc_descriptor(descriptor=descriptor, configs=configs, ase_atoms_list=ase_atoms_list,
desc_file='lasso_l0_binaries_example.tar.gz', format_geometry='aims', selected_feature_list=selected_feature_list, nb_jobs=-1)
# load descriptor target_list, structure_list = load_descriptor(desc_files=desc_file_path, configs=configs) df_atomic_features = get_table_atomic_features(structure_list)
# ============================================================================= # Model calculation # =============================================================================
chemical_formulas = [structure.get_chemical_formula(mode='hill') for structure in structure_list] df_atomic_features['chemical_formula'] = chemical_formulas df_atomic_features = df_atomic_features.sort_values(by='chemical_formula').reset_index(drop=True)
# target values to predict dict_delta_e = dict(SeZn=0.2631369195046646, BaTe=-0.37538683850924387, BN=1.7120803923951688, CGe=0.8114429425515818, GaP=0.3487518245522925, MgS=-0.08669951164989079, GaN=0.4334452723999156, AlAs=0.21326186549251072, BP=1.019225239514441, FK=-0.14640610974868423, BrLi=-0.03274621540254649, BSb=0.5808491589999847, CaTe=-0.3504563060008138, ClK=-0.16446069285018655, BrCs=-0.1558673149861294, BrCu=0.15244265149855352, ILi=-0.021660938008450818, CuF=-0.01702227364862989, FNa=-0.14578814899027592, C2=2.6286038411199026, AgBr=-0.030033419005850936, CuI=0.20467459898973175, GaSb=0.15462529698986593, ClLi=-0.03838148564873346, AsIn=0.13404758548892423, OZn=0.10196818460305757, MgO=-0.2322747421651549, InP=0.17919330099729866, Ge2=0.20085254149716641, InN=0.15372030450150198, CSn=0.45353800899655555, CdTe=0.11453954098812649, TeZn=0.24500131400199776, MgTe=-0.004591286999846332, BaS=-0.3197624539995756, CaSe=-0.36079776214906895, FRb=-0.1355957874033439, BeO=0.6918376303948839, AsB=0.8749782510022386, CaS=-0.36913322290101264, CaO=-0.2652190617003161, BaO=-0.09299856100784433, AlSb=0.15686874600534004, SrTe=-0.3792947550252322, BeS=0.5063277134499351, InSb=0.0780598790169251, SZn=0.27581334679854935, OSr=-0.2203066401004525, BrRb=-0.1638205440075271, BeSe=0.4949404808020511, ClRb=-0.16050356640655905, BrNa=-0.1264287376032476, MgSe=-0.05530180620975655, GeSn=0.08166336650886348, GeSi=0.2632101904042582, CsF=-0.10826332699038382, CdSe=0.08357195550137826, FLi=-0.059488321434879074, AlN=0.07294907877519896, Si2=0.2791658430004932, SiSn=0.13510880949563495, ClNa=-0.13299199530041886, CdO=-0.0841613645001312, SSr=-0.36843415824218, IK=-0.16703915799644553, BaSe=-0.3434451604764059, BrK=-0.1661759769597461, BeTe=0.4685859464949282, CdS=0.07267280149604124, CsI=-0.16238748698990838, INa=-0.11483823100687315, AlP=0.2189583583002711, AsGa=0.27427779349540243, SeSr=-0.3745109805057823, CSi=0.669023778644634, AgCl=-0.04279728149250233, AgI=0.03692542249419624, AgF=-0.15375768499313544, ClCs=-0.1503461689991465, Sn2=0.016963900503544026, ClCu=0.15625872520000064, IRb=-0.16720145498980848)
df_atomic_features['target'] = df_atomic_features['chemical_formula'].map(dict_delta_e) target = np.asarray(df_atomic_features['target'].values.astype(float))
cols_to_drop = ['chemical_formula', 'target', 'ordered_chemical_symbols']
# use the l1-l0 method proposed in Ghiringhelli et al. (2015) calc_model(method='l1_l0', df_features=df_atomic_features, cols_to_drop=cols_to_drop, target=target, max_dim=2, allowed_operations=allowed_operations, tmp_folder=configs['io']['tmp_folder'], results_folder=configs['io']['results_folder'], lookup_file=lookup_file, control_file=configs['io']['control_file'], energy_unit='eV', length_unit='angstrom')
# read the results for the two-dimensional descriptor viewer_filename = 'l1_l0_dim1_for_viewer.csv' viewer_filepath = os.path.join(configs['io']['results_folder'], viewer_filename) df_viewer = pd.read_csv(viewer_filepath) x_axis_label, y_axis_label = read_control_file(configs['io']['control_file'])
# plot the results for the two-dimensional descriptor fig, ax = plt.subplots() x = df_viewer['coord_0'] y = df_viewer['coord_1'] color = df_viewer['y_true'] chemical_formula = df_viewer['chemical_formula'] cm = plt.cm.get_cmap('rainbow') sc = plt.scatter(x, y, c=color, cmap=cm)
# annotate the points for i, txt in enumerate(chemical_formula): ax.annotate(txt, (x[i], y[i]), size=4)
plt.xlabel(x_axis_label) plt.ylabel(y_axis_label) cbar = plt.colorbar(sc) cbar.set_label('Reference E(RS)-E(ZB)', rotation=90) plt.title("l1/l0 structure map for binary compoundsn ") plt.subplots_adjust(bottom=0.2) plt.figtext(0.5, 0.02, "Compare with Fig. 2 in Ghiringhelli et al., Phys. Rev. Lett 114 (10), 105503 (2015)", horizontalalignment='center', style='italic')
plt.savefig(materials_map_plot_file, dpi=300)
This is the plot showing the calculated energy differences between rocksalt and zincblende structures of the 82 octet binary AB materials used in Ref.2 according to the two-dimensional descriptor found via the LASSO+l0 procedure:
Implementation details of how atomic features are automatically constructed can be found at :pyai4materials.descriptors.atomic_features. Implementation details of the LASSO+l0 method can be found at :pyai4materials.wrappers.calc_model and at :pyai4materials.models.l1_l0.
ai4materials.models.cnn-nature-comm2018
This example shows how to load a dataset of crystal structures (represented by the diffraction fingerprint3), train a convolutional neural network on pristine (perfect) crystal structures, and use this neural network to predict the crystal class of highly defective crystal structures. This method - introduced in Ref.4 - allows to correctly classify heavily defective crystal structures. In this particular case, even if 25% of the atoms were removed from each structure, the model still retains an accuracy of 100%.
The code below performs following steps:
- read the dataset from crystal-structure classification used in Ref.5
- train a convolutional neural network for crystal-structure classification using :py
ai4materials.models.cnn_nature_comm_ziletti2018.train_neural_network - predict the class for each crystal structure using the neural network trained in in Ref.6 using :py
ai4materials.models.cnn_nature_comm_ziletti2018.predict
from functools import partial from ai4materials.utils.utils_config import set_configs from ai4materials.dataprocessing.preprocessing import load_dataset_from_file from ai4materials.models.cnn_architectures import cnn_nature_comm_ziletti2018 from ai4materials.models.cnn_nature_comm_ziletti2018 import load_datasets from ai4materials.models.cnn_nature_comm_ziletti2018 import predict from ai4materials.models.cnn_nature_comm_ziletti2018 import train_neural_network from ai4materials.utils.utils_config import setup_logger import numpy as np import os
configs = set_configs() logger = setup_logger(configs, level='DEBUG', display_configs=False) dataset_folder = configs['io']['main_folder']
# ============================================================================= # Download the dataset from the online repository and load it # =============================================================================
x_pristine, y_pristine, dataset_info_pristine, x_vac25, y_vac25, dataset_info_vac25 = load_datasets(dataset_folder)
train_set_name = 'pristine_dataset' path_to_x_pristine = os.path.join(dataset_folder, train_set_name + '_x.pkl') path_to_y_pristine = os.path.join(dataset_folder, train_set_name + '_y.pkl') path_to_summary_pristine = os.path.join(dataset_folder, train_set_name + '_summary.json')
test_set_name = 'vac25_dataset' path_to_x_vac25 = os.path.join(dataset_folder, test_set_name + '_x.pkl') path_to_y_vac25 = os.path.join(dataset_folder, test_set_name + '_y.pkl') path_to_summary_vac25 = os.path.join(dataset_folder, test_set_name + '_summary.json')
- x_pristine, y_pristine, dataset_info_pristine = load_dataset_from_file(path_to_x_pristine, path_to_y_pristine,
path_to_summary_pristine)
- x_vac25, y_vac25, dataset_info_vac25 = load_dataset_from_file(path_to_x_vac25, path_to_y_vac25,
path_to_summary_vac25)
# ============================================================================= # Train the convolutional neural network # =============================================================================
# load the convolutional neural network architecture from Ziletti et al., Nature Communications 9, pp. 2775 (2018) partial_model_architecture = partial(cnn_nature_comm_ziletti2018, conv2d_filters=[32, 32, 16, 16, 8, 8], kernel_sizes=[3, 3, 3, 3, 3, 3], max_pool_strides=[2, 2], hidden_layer_size=128)
# use x_train also for validation - this is only to run the test results = train_neural_network(x_train=x_pristine, y_train=y_pristine, x_val=x_pristine, y_val=y_pristine, configs=configs, partial_model_architecture=partial_model_architecture, nb_epoch=1)
text_labels = np.asarray(dataset_info_vac25["data"][0]["text_labels"])[:100] numerical_labels = np.asarray(dataset_info_vac25["data"][0]["numerical_labels"])[:100]
# ============================================================================= # Predict the crystal class of a material using the trained neural network # =============================================================================
# load the convolutional neural network architecture from Ziletti et al., Nature Communications 9, pp. 2775 (2018) # you can also use your own neural network to predict, passing it to the variable 'model' results = predict(x_vac25, y_vac25, configs=configs, numerical_labels=numerical_labels, text_labels=text_labels, model=None)
This is the confusion matrix obtained using the convolutional neural network to predict the class of structures with 25% of missing atoms:
The model has an accuracy of 100%, even in the presence of defects (25% atoms missing in this case). The neural network's training and prediction is performed with Keras. Implementation details on the convolutional neural network used can be found at :pyai4materials.models.cnn_nature_comm_ziletti2018.
Angelo Ziletti <angelo.ziletti@gmail.com>
ai4materials.models.clustering ai4materials.models.cnn_architectures ai4materials.models.cnn_nature_comm_ziletti2018 ai4materials.models.cnn_polycrystals ai4materials.models.embedding ai4materials.models.l1_l0 ai4materials.models.sis ai4materials.models.strided_pattern_matching
ai4materials.models
L. M. Ghiringhelli, J. Vybiral, S. V. Levchenko, C. Draxl, and M. Scheffler, “Big Data of Materials Science: Critical Role of the Descriptor,” Physical Review Letters, vol. 114, no. 10, p. 105503 . [Link to article]↩
L. M. Ghiringhelli, J. Vybiral, S. V. Levchenko, C. Draxl, and M. Scheffler, “Big Data of Materials Science: Critical Role of the Descriptor,” Physical Review Letters, vol. 114, no. 10, p. 105503 . [Link to article]↩
A. Ziletti, D. Kumar, M. Scheffler, and L. M. Ghiringhelli, "Insightful classification of crystal structures using deep learning," Nature Communications, vol. 9, pp. 2775, 2018. [Link to article]↩
A. Ziletti, D. Kumar, M. Scheffler, and L. M. Ghiringhelli, "Insightful classification of crystal structures using deep learning," Nature Communications, vol. 9, pp. 2775, 2018. [Link to article]↩
A. Ziletti, D. Kumar, M. Scheffler, and L. M. Ghiringhelli, "Insightful classification of crystal structures using deep learning," Nature Communications, vol. 9, pp. 2775, 2018. [Link to article]↩
A. Ziletti, D. Kumar, M. Scheffler, and L. M. Ghiringhelli, "Insightful classification of crystal structures using deep learning," Nature Communications, vol. 9, pp. 2775, 2018. [Link to article]↩