Computational Design of Stable and Highly Ion-conductive Materials using Multi-objective Bayesian Optimization: Case Studies on Diffusion of Oxygen and Lithium

Ion-conducting solid electrolytes are widely used for a variety of purposes. Therefore, designing highly ion-conductive materials is in strongly demand. Because of advancement in computers and enhancement of computational codes, theoretical simulations have become effective tools for investigating the performance of ion-conductive materials. However, an exhaustive search conducted by theoretical computations can be prohibitively expensive. Further, for practical applications, both dynamic conductivity as well as static stability must be satisfied at the same time. Therefore, we propose a computational framework that simultaneously optimizes dynamic conductivity and static stability; this is achieved by combining theoretical calculations and the Bayesian multi-objective optimization that is based on the Pareto hyper-volume criterion. Our framework iteratively selects the candidate material, which maximizes the expected increase in the Pareto hyper-volume criterion; this is a standard optimality criterion of multi-objective optimization. Through two case studies on oxygen and lithium diffusions, we show that ion-conductive materials with high dynamic conductivity and static stability can be efficiently identified by our framework.

Active-learning-based efficient prediction of ab-initio atomic energy: a case study on a Fe random grain boundary model with millions of atoms

We have developed a method that can analyze large random grain boundary (GB) models with the accuracy of density functional theory (DFT) calculations using active learning. It is assumed that the atomic energy is represented by the linear regression of the atomic structural descriptor. The atomic energy is obtained through DFT calculations using a small cell extracted from a huge GB model, called replica DFT atomic energy. The uncertainty reduction (UR) approach in active learning is used to efficiently collect the training data for the atomic energy. In this approach, atomic energy is not required to search for candidate points; therefore, sequential DFT calculations are not required. This approach is suitable for massively parallel computers that can execute a large number of jobs simultaneously. In this study, we demonstrate the prediction of the atomic energy of a Fe random GB model containing one million atoms using the UR approach and show that the prediction error decreases more rapidly compared with random sampling. We conclude that the UR approach with replica DFT atomic energy is useful for modeling huge GBs and will be essential for modeling other structural defects.

Safe Pattern Pruning: An Efficient Approach for Predictive Pattern Mining

In this paper we study predictive pattern mining problems where the goal is to construct a predictive model based on a subset of predictive patterns in the database. Our main contribution is to introduce a novel method called safe pattern pruning (SPP) for a class of predictive pattern mining problems. The SPP method allows us to efficiently find a superset of all the predictive patterns in the database that are needed for the optimal predictive model. The advantage of the SPP method over existing boosting-type method is that the former can find the superset by a single search over the database, while the latter requires multiple searches. The SPP method is inspired by recent development of safe feature screening. In order to extend the idea of safe feature screening into predictive pattern mining, we derive a novel pruning rule called safe pattern pruning (SPP) rule that can be used for searching over the tree defined among patterns in the database. The SPP rule has a property that, if a node corresponding to a pattern in the database is pruned out by the SPP rule, then it is guaranteed that all the patterns corresponding to its descendant nodes are never needed for the optimal predictive model. We apply the SPP method to graph mining and item-set mining problems, and demonstrate its computational advantage.

Simultaneous Safe Screening of Features and Samples in Doubly Sparse Modeling

The problem of learning a sparse model is conceptually interpreted as the process of identifying active features/samples and then optimizing the model over them. Recently introduced safe screening allows us to identify a part of non-active features/samples. So far, safe screening has been individually studied either for feature screening or for sample screening. In this paper, we introduce a new approach for safely screening features and samples simultaneously by alternatively iterating feature and sample screening steps. A significant advantage of considering them simultaneously rather than individually is that they have a synergy effect in the sense that the results of the previous safe feature screening can be exploited for improving the next safe sample screening performances, and vice-versa. We first theoretically investigate the synergy effect, and then illustrate the practical advantage through intensive numerical experiments for problems with large numbers of features and samples.