[Paper Review] Reduced collinearity, low-dimensional cluster expansion model for adsorption of halides (Cl, Br) on Cu(100) surface using principal component analysis

Bibek Dash, Suhail Haque+1 more|arXiv (Cornell University)|Jul 21, 2023

Machine Learning in Materials Science4 citations

TL;DR

This paper proposes a principal component analysis (PCA)-based cluster expansion model (CEM) to overcome collinearity and data scarcity in modeling halide (Cl, Br) adsorption on Cu(100). By transforming correlated cluster interactions into uncorrelated principal components, the method enables accurate CEM construction with only 8 density functional theory (DFT) energies, yielding a low-dimensional model with 10 effective cluster interactions that matches experimental thermodynamic behavior.

ABSTRACT

The cluster expansion model (CEM) provides a powerful computational framework for rapid estimation of configurational properties in disordered systems. However, the traditional CEM construction procedure is still plagued by two fundamental problems: (i) even when only a handful of site cluster types are included in the model, these clusters can be correlated and therefore they cannot independently predict the material property, and (ii) typically few tens-hundreds of datapoints are required for training the model. To address the first problem of collinearity, we apply the principal component analysis method for constructing a CEM. Such an approach is shown to result in a low-dimensional CEM that can be trained using a small DFT dataset. We use the ab initio thermodynamic modeling of Cl and Br adsorption on Cu(100) surface as an example to demonstrate these concepts. A key result is that a CEM containing 10 effective cluster interactions build with only 8 DFT energies (note, number of training configurations > number of principal components) is found to be accurate and the thermodynamic behavior obtained is consistent with experiments. This paves the way for construction of high-fidelity CEMs with sparse/limited DFT data.

Motivation & Objective

• To address the persistent issue of collinearity among cluster interactions in traditional cluster expansion models (CEMs), which hinders independent prediction of material properties.
• To reduce the data requirements for training CEMs by leveraging dimensionality reduction, especially when only sparse DFT data is available.
• To develop a low-dimensional CEM that maintains high accuracy while minimizing the number of training configurations.
• To demonstrate the feasibility of constructing high-fidelity CEMs from limited DFT datasets using PCA-based feature transformation.
• To validate the model’s predictive power by comparing its thermodynamic predictions with experimental data for Cl and Br adsorption on Cu(100).

Proposed method

• Apply principal component analysis (PCA) to transform correlated cluster interaction vectors into a set of uncorrelated principal components, reducing collinearity.
• Use the principal components as basis functions for constructing a low-dimensional cluster expansion model (CEM) instead of raw cluster interactions.
• Train the CEM using only 8 DFT-calculated adsorption energies, demonstrating success with fewer data points than traditional methods.
• Select the number of principal components based on explained variance, ensuring model fidelity while minimizing dimensionality.
• Reconstruct the original cluster interactions from the principal components to interpret physical contributions to adsorption energy.
• Validate the model by comparing predicted thermodynamic properties (e.g., surface coverage, free energy) with experimental trends.

Experimental results

Research questions

• RQ1 Can PCA effectively reduce collinearity among cluster interactions in a cluster expansion model for surface adsorption systems?
• RQ2 To what extent can a CEM trained on a minimal DFT dataset (e.g., 8 energies) maintain predictive accuracy for halide adsorption on Cu(100)?
• RQ3 Does the PCA-based CEM reproduce experimentally observed thermodynamic trends for Cl and Br adsorption on Cu(100)?
• RQ4 How many principal components are sufficient to capture the essential physics of halide adsorption with minimal model complexity?
• RQ5 Can the resulting low-dimensional CEM be interpreted in terms of physically meaningful cluster interactions?

Key findings

• A cluster expansion model built from 10 effective cluster interactions using only 8 DFT energies achieved high accuracy in predicting adsorption thermodynamics for Cl and Br on Cu(100).
• The PCA-based method successfully reduced collinearity among cluster interactions, enabling stable and independent parameter estimation despite limited training data.
• The model's predicted surface coverage and free energy trends were consistent with experimental observations, validating its predictive power.
• The number of training configurations (8) exceeded the number of principal components used, satisfying the condition for reliable model training.
• The resulting low-dimensional CEM demonstrated that high-fidelity modeling is feasible even with sparse DFT data, significantly reducing computational cost.
• The approach enables the construction of accurate CEMs in systems where traditional methods fail due to data scarcity or high correlation among clusters.