Explainable machine learning for materials discovery: predicting the potentially formable Nd-Fe-B crystal structures and extracting the structure-stability relationship.

New Nd-Fe-B crystal structures can be formed via the elemental substitution of LA-T-X host structures, including lanthanides (LA), transition metals (T) and light elements, X = B, C, N and O. The 5967 samples of ternary LA-T-X materials that are collected are then used as the host structures. For each host crystal structure, a substituted crystal structure is created by substituting all lanthanide sites with Nd, all transition metal sites with Fe and all light-element sites with B. High-throughput first-principles calculations are applied to evaluate the phase stability of the newly created crystal structures, and 20 of them are found to be potentially formable. A data-driven approach based on supervised and unsupervised learning techniques is applied to estimate the stability and analyze the structure-stability relationship of the newly created Nd-Fe-B crystal structures. For predicting the stability for the newly created Nd-Fe-B structures, three supervised learning models: kernel ridge regression, logistic classification and decision tree model, are learned from the LA-T-X host crystal structures; the models achieved maximum accuracy and recall scores of 70.4 and 68.7%, respectively. On the other hand, our proposed unsupervised learning model based on the integration of descriptor-relevance analysis and a Gaussian mixture model achieved an accuracy and recall score of 72.9 and 82.1%, respectively, which are significantly better than those of the supervised models. While capturing and interpreting the structure-stability relationship of the Nd-Fe-B crystal structures, the unsupervised learning model indicates that the average atomic coordination number and coordination number of the Fe sites are the most important factors in determining the phase stability of the new substituted Nd-Fe-B crystal structures.

Committee machine that votes for similarity between materials.

A method has been developed to measure the similarity between materials, focusing on specific physical properties. The information obtained can be utilized to understand the underlying mechanisms and support the prediction of the physical properties of materials. The method consists of three steps: variable evaluation based on nonlinear regression, regression-based clustering, and similarity measurement with a committee machine constructed from the clustering results. Three data sets of well characterized crystalline materials represented by critical atomic predicting variables are used as test beds. Herein, the focus is on the formation energy, lattice parameter and Curie temperature of the examined materials. Based on the information obtained on the similarities between the materials, a hierarchical clustering technique is applied to learn the cluster structures of the materials that facilitate interpretation of the mechanism, and an improvement in the regression models is introduced to predict the physical properties of the materials. The experiments show that rational and meaningful group structures can be obtained and that the prediction accuracy of the materials' physical properties can be significantly increased, confirming the rationality of the proposed similarity measure.

Learning structure-property relationship in crystalline materials: A study of lanthanide-transition metal alloys.

We have developed a descriptor named Orbital Field Matrix (OFM) for representing material structures in datasets of multi-element materials. The descriptor is based on the information regarding atomic valence shell electrons and their coordination. In this work, we develop an extension of OFM called OFM1. We have shown that these descriptors are highly applicable in predicting the physical properties of materials and in providing insights on the materials space by mapping into a low embedded dimensional space. Our experiments with transition metal/lanthanide metal alloys show that the local magnetic moments and formation energies can be accurately reproduced using simple nearest-neighbor regression, thus confirming the relevance of our descriptors. Using kernel ridge regressions, we could accurately reproduce formation energies and local magnetic moments calculated based on first-principles, with mean absolute errors of 0.03 µB and 0.10 eV/atom, respectively. We show that meaningful low-dimensional representations can be extracted from the original descriptor using descriptive learning algorithms. Intuitive prehension on the materials space, qualitative evaluation on the similarities in local structures or crystalline materials, and inference in the designing of new materials by element substitution can be performed effectively based on these low-dimensional representations.

Novel mixture model for the representation of potential energy surfaces.

We demonstrate that knowledge of chemical physics on a materials system can be automatically extracted from first-principles calculations using a data mining technique; this information can then be utilized to construct a simple empirical atomic potential model. By using unsupervised learning of the generative Gaussian mixture model, physically meaningful patterns of atomic local chemical environments can be detected automatically. Based on the obtained information regarding these atomic patterns, we propose a chemical-structure-dependent linear mixture model for estimating the atomic potential energy. Our experiments show that the proposed mixture model significantly improves the accuracy of the prediction of the potential energy surface for complex systems that possess a large diversity in their local structures.

Data mining for materials design: a computational study of single molecule magnet.

We develop a method that combines data mining and first principles calculation to guide the designing of distorted cubane Mn(4+)Mn3(3+) single molecule magnets. The essential idea of the method is a process consisting of sparse regressions and cross-validation for analyzing calculated data of the materials. The method allows us to demonstrate that the exchange coupling between Mn(4+) and Mn(3+) ions can be predicted from the electronegativities of constituent ligands and the structural features of the molecule by a linear regression model with high accuracy. The relations between the structural features and magnetic properties of the materials are quantitatively and consistently evaluated and presented by a graph. We also discuss the properties of the materials and guide the material design basing on the obtained results.