Pdn-CE

Pdn cluster expansion (CE)

LASSO-assisted-Cluster-Expansion

The cluster expansion (CE) model is trained on Pdn clusters supported on Ceria. The model can be used to predict energy for any given cluster structures on a unit cell.

Training

Model is training is performed by train_lasso.py

Usage

See test_model_usage.py for details

• Predict the energy for structures in configuration dataset on a 5 by 5 lattice (mother)

from set_config_constants import config
from set_ce_lattice import mother
import energy_functions as energy
from set_ce_lattice import dz
from generate_clusters_super_cell import super_mother

# Load energy object
Pdn = energy.Pdn(lasso_file, mother=mother, super_cell_flag=False)

# select a Pd single atom from configuration dataset
config_SA = config[0][0]

# Predict energy for a single atom
E_pred_SA, _  = Pdn.predict_E(config_SA)

# Visualize the atomic configuration
atoms_SA = energy.append_support(config_SA, mother, view_flag=True)

• Generate a random structure and calculate its energy on a 10 by 10 lattice (super_mother)

from set_config_constants import config
from set_ce_lattice import mother
import energy_functions as energy
from set_ce_lattice import dz
from generate_clusters_super_cell import super_mother

# Load energy object
Pdn_super = energy.Pdn(lasso_file, mother=super_mother, super_cell_flag=True)

# Single atoms to put on the base layer
n_seeds = 20

# the index for base layer atoms in super cell
base_indices = np.where(super_mother[:,2] == dz)[0]
base_occ_indices = np.unique(np.random.choice(base_indices, n_seeds, replace = False))


# Initialize the individual configuration in one hot encoding
rnd_individual = np.zeros(len(super_mother),dtype = int)
rnd_individual[base_occ_indices] = 1


# Predict energy for initial configuration
config_rnd = energy.one_hot_to_index(rnd_individual)
E_pred_rnd, _  = Pdn_super.predict_E(config_rnd)

# Visualize the atomic configuration
atoms_rnd = energy.append_support(config_rnd, super_mother, view_flag=True)

Reading more

• Dataset and description

GitHub repository

• Publication

Wang, Y., Su, Y., Hensen, E. J. M., & Vlachos, D. G. (2020). Finite-Temperature Structures of Supported Subnanometer Catalysts Inferred via Statistical Learning and Genetic Algorithm-Based Optimization. ACS Nano. https://doi.org/10.1021/acsnano.0c06472