Physics Interpretable Ensemble Learning for Materials Property Prediction: Carbon as an Example

Machine learning models especially neural networks are most efficient and accurate methods to predict materials properties. But training a neural network model is time-consuming and often involves numerous parameters of little physical interpretability. Furthermore, input descriptors (if complicated) need to be designed manually to satisfy certain physical constraints such as of permutation, rotation, and reflection invariances. Here we propose an ensemble learning model consisting of regression trees to predict materials properties, using the formation energy and elastic constants of carbon allotropes as examples. Instead of using descriptors, our model adopts the computed energy and elastic constants from nine different classical interatomic potentials as inputs. The results of ensemble learning are more accurate than those from individual classical interatomic potentials, if density functional theory (DFT) results are used as the references. Because of the correlation between inputs and DFT reference, the regression trees can extract the relatively accurate formation energy or elastic constant that is calculated by the nine classical potentials and used as criteria for predicting the final properties. Our work shows the ensemble learning is applicable to different crystal structures while retaining physical interpretability to some extent.