In machine learning, splitting data into training and test sets is usually achieved using random stratified sampling, in which classes are proportionally divided into two subsets. Other methods also consider feature-aware criteria, and some of those methods claim to have achieved optimal split of minimised variance. We do not advocate aiming to achieve an optimal split or minimise variance since this would be counterproductive for ensemble methods, where the diversity of the training set is desired. Ensemble methods achieve diversity through bagging and boosting schemes. In the recently introduced Monte Carlo ensemble approach, diversity can be maintained through random stratified sampling without using bagging or boosting methods. This work introduces a feature-aware split that retains the diversity of the ensemble. To this end, we propose an evolutionary algorithm that starts with an entirely random population and aims at objectives of proportional class-representation and minimisation of the normalized mean error rather than minimisation of variance. The proposed data-split method is tested on three different models used within a hierarchical Monte Carlo ensemble. The results show that the method positively affects the predictability performance when applied on two domain-specific material science datasets and a collection of 38 general machine learning datasets.

Geometry optimization of atomic structures is a common and crucial task in computational chemistry and materials design. Following the learning to optimize paradigm, we propose a new multi-agent reinforcement learning method called Multi-Agent Crystal Structure optimization (MACS) to address the problem of periodic crystal structure optimization. MACS treats geometry optimization as a partially observable Markov game in which atoms are agents that adjust their positions to collectively discover a stable configuration. We train MACS across various compositions of reported crystalline materials to obtain a policy that successfully optimizes structures from the training compositions as well as structures of larger sizes and unseen compositions, confirming its excellent scalability and zero-shot transferability. We benchmark our approach against a broad range of state-of-the-art optimization methods and demonstrate that MACS optimizes periodic crystal structures significantly faster, with fewer energy calculations, and the lowest failure rate.

This paper presents the theory of probabilistic hier-archical supervised ensemble learning (TPHSEL), a classification approach we have developed with the goal of obtaining classifications for material selection with a degree of interpretability of the results. We found that TPHSEL is a competitive classifier, not only for our target application, but also for a broader range of standard datasets, where it outperformed support vector machines, random forests, and optimal classification trees. The dataset we developed the method for within the field of materials science is small (405 entries), leading to relatively low accuracy (81 % to 82 %) for both our method and a deep learning approach used earlier. In this context, we found that selection based on a large vote share left close to 20 % of candidate materials, and in this bracket, accuracy and other model performance metrics are above 0.95. This is excellent news for prioritising experimental targets (and related tasks), as it indicates that it is possible to identify promising candidates based on data that still leaves shortfalls in classification.

This paper presents hierarchical supervised Monte Carlo ensemble learning (HSMEL). This provides an extension to the theory of probabilistic hierarchical supervised ensemble learning (TPHSEL), which itself evolved from the theory of prob-abilistic hierarchical supervised learning (TPHSL). The basic idea captured in TPHSL is that a complex model can be replaced with a hierarchy of simple and mathematically understandable models. Such models are amenable to interpretation, and they are therefore more likely to contribute to explainable AI, in comparison to black box models. The basic TPHSL was subsequently advanced to TPHSEL, where several hierarchical models make a classification decision by majority vote. In this paper TPHSEL is further advanced to include the notion of Monte Carlo ensemble. We show that this ensemble is computationally faster and has broader reach on training examples. The method has been deployed in use cases from materials science, specifically to study the impact of various features on the conductivity of materials. Based on the performance of individual features, the method has been devised that applies set theory over ensemble outcomes to predict the average accuracy that could be achieved if those features are grouped in some way. We argue that this method has potential to accelerate material design procedures by providing predictions about machine learning performance parameters without engaging in extensive computational effort and consequently will also reduce chemistry lab experimentation. In addition, to show resilience of HSMEL, we have also applied it on 28 general machine learning datasets, where its performance is compared with the classical methods from the literature.