Explainable Machine Learning for Oxygen Diffusion in Perovskites and Pyrochlores

TL;DR

This work tackles predicting oxygen diffusion activation energies in perovskites and pyrochlores using explainable ML. The authors build a labeled database of experimental activation energies, derive grouped, site-specific MAGPIE features, and train seven diverse models, employing a grouping-based feature importance method and SHAP explanations. They find that for perovskites the A-site bond ionicity and $p_{O_2}$ are the most predictive, whereas for pyrochlores the A-site $s$-valence count and B-site electronegativity dominate, with oxide-binary-derived features often less informative than elemental-weighted averages. The approach yields linear relationships in many cases, reveals meaningful design rules for fast oxide-ion diffusion, and provides uncertainty estimates, enabling rapid screening of new oxides for solid oxide fuel cells.

Abstract

Explainable machine learning can help to discover new physical relationships for material properties. To understand the material properties that govern the activation energy for oxygen diffusion in perovskites and pyrochlores, we build a database of experimental activation energies and apply a grouping algorithm to the material property features. These features are then used to fit seven different machine learning models. An ensemble consensus determines that the most important features for predicting the activation energy are the ionicity of the A-site bond and the partial pressure of oxygen for perovskites. For pyrochlores, the two most important features are the A-site $s$ valence electron count and the B-site electronegativity. The most important features are all constructed using the weighted averages of elemental metal properties, despite weighted averages of the constituent binary oxides being included in our feature set. This is surprising because the material properties of the constituent oxides are more similar to the experimentally measured properties of perovskites and pyrochlores than the features of the metals that are chosen. The easy-to-measure features identified in this work enable rapid screening for new materials with fast oxide-ion diffusivity.

Figures (11)

• Figure 1: Count of the elements included in the perovskites (left) and pyrochlores (right) database split by site. For perovskites, La is the most common element contained in 62 perovskites, followed by Ga with 60 and Sr with 57. Zr is the most common element in the pyrochlore database, occurring in the B site for 34 pyrochlores.
• Figure 2: Hierarchical grouping of site A features using the Ward variance minimization. For all oxides, we use the weighted average (mean) of the elemental features by atomic composition without oxygen and the standard deviations (dev) of the MAGPIE features. The six features with the oxide label are combinations of the oxide building blocks. We use the Spearman rank correlations to define the distance between features, shown in the upper triangle of the right panel; the lower triangle provides the Pearson correlations. Using a greedy algorithm that groups the two closest features at every step, Ward variance minimization create groups of correlated features in the left panel. We chose a distance threshold of 1.2 to define groups, which are separated by black lines. The representative features for each group are bolded in the labels on the left and used as labels in the correlation plot. These are chosen through a greedy algorithm that chooses each feature with the highest correlation with a residual of a linear model with the activation energy and all previously chosen features.
• Figure 3: Hierarchical grouping of site B features using the Ward variance minimization. For all oxides, we use the weighted average (mean) of the elemental features by atomic composition without oxygen and the standard deviations (dev) of the MAGPIE features. The six features with the oxide label are combinations of the constituent binary oxides. We use the Spearman rank correlations to define the distance between features, shown in the upper triangle of the right panel; the lower triangle provides the Pearson correlations. Using a greedy algorithm that groups the two closest features at every step, Ward variance minimization creates groups of correlated features in the left panel. We choose a distance threshold of 1.2 to define groups, which are separated by black lines. The representative features for each group are bolded in the labels on the left and used as labels in the correlation plot. These are chosen through a greedy algorithm that chooses each feature with the highest correlation with a residual of a linear model with the activation energy and all previously chosen features. Site B features have a more pronounced block structure than their site A counterparts, and there are much weaker correlations between the top two and bottom two feature groups.
• Figure 4: Predicted vs. experimental activation energies for oxygen in both perovskites and pyrochlores. In the middle and bottom rows, we plot only predictions on the test set over all cross-validation splits, and no training data is shown. The color denotes the crystal structure of the oxide. The two linear models, Bayesian Ridge and linear, have comparable RMSEs (162--168 meV) compared to the other five non-linear models (147--161 meV). This is despite major differences in the features and diffusion mechanism between the two crystal structures, so we can conclude that the differences can be accurately represented by a linear relationship.
• Figure 5: Predicted vs. experimental activation energies for oxygen in perovskites. The marker shape denotes the partial pressure of oxgyen ($p_{\text{O}_2}$) of the experimental measurements. In the middle and bottom rows, we plot only predictions on the test set over all cross-validation splits, and no training data is shown. Our models have RMSEs (199 meV) for activation energies measured at high $p_{\text{O}_2}$ (20%) that are almost twice as large as those measured at near vacuum (107 meV), likely due to the smaller amount of data at high $p_{\text{O}_2}$ . More complex models, like the Gaussian process or gradient boosting trees, perform the worst on this dataset as their higher flexibilities lead to overfitting.