Structure prediction of two-dimensional materials based on neural network-driven evolutionary technique

Abstract

We present a simple yet effective method for structure prediction of two-dimensional structures. The method is based on a combination of neural networks and evolutionary techniques. It allows finding pristine 2D structures as well as structures grown on a substrate. Conducted tests show that the method is efficient and the calculations, based only on the information of stoichiometry, can lead to stable structures. Since the algorithm is able to address structures on a given substrate, it can be useful from the experimental point of view.

Introduction

These days, making an attempt to find a perfect combination of chemicals suitable for specific applications, a chemist (or a materials engineer) has two options. The first one is to conduct an experiment, synthesize a sample, and then characterize it with proper methods. The second option is to use a theoretical study first, which may reveal properties of a given material with very high credibility. This is possible mainly due to the huge success of the ab-initio methods, based on Density Functional Theory (DFT) [1], which is currently one of the main computational tools for materials sciences, used at the atomic level. Increasing computational power and data storage capacity have made possible the calculation and analysis of properties for a huge amount of materials. That high throughput (HT) studies (e.g. [2]) are becoming more and more popular because at relatively low cost of these allow scientists to pick out structures with desirable properties from a large group of average ones. Moreover, large amounts of generated data inspired studies based on methods used earlier in pure data science, such as deep learning methods [3], usually based on artificial neural networks (NN) [4] and evolutionary optimization methods [5]. An additional effect of these HT studies is the creation of free-accessible on-line databases [6], [7], containing thousands of calculated structures.

From the implementation point of view of the previously mentioned methods, one may observe three main directions. First one is the application of the methods based on evolutionary algorithms, as implemented for example in XtalOpt [8] or USPEX codes [9]. Especially the latter was extremely successful, being used in more than half a thousand studies. The second direction one may take is a swarm optimization [10], implemented for example in the CALYPSO code [11]. A third way is the use of (more and more popular in all fields of science) artificial neural networks.

A machine learning (ML) approach is today a well established branch of materials science [12]. These studies take advantage of the large amount of available data to train the network and then use it to predict properties of yet unknown structures. For example, a thorough studies were conduced for the structure prediction of binary [13] and ternary compounds [14]. Also, in the study [15], a ML model has been trained to discover Heusler compounds with a true positive rate of 0.94. Moreover, according to [16], it is possible to build a NN model, which predicts crystals’ properties with greater accuracy (with respect to an experiment) than a Hybrid DFT method does. One of the disadvantages of this approach, though, is the necessity of having the proper set of data, on which the NN would learn.

It is also possible to combine methods belonging to one of the aforementioned paths. Especially promising (e.g. in terms of performance) seem to be methods combining NN and evolutionary approach [17]. In these hybrid methods, NN and DFT evaluations of the total energy are used in the pursuit of the optimal structure.

Low-dimensional materials play an increasingly important role in the pursuit of the new generation of structures that will build future logic systems. Extensive theoretical work on this subject work resulted in significant number of potentially valuable substances. Similarly, significant progress has been made in the experimental field [18]. Also, very recently, the first two-dimensional (2D) magnetic material has been experimentally confirmed [19]. These materials are not only flat as graphene but may also be built of several monoatomic layers [18]. Also, experimentally, a 2D layer is always placed on a substrate, so theoretical models have to include its impact.

In this paper, we present a simple, yet effective algorithm of finding new two dimensional structures, either in vacuum or on a substrate, starting only with its stoichiometry. Since the main issue of the new materials search problem is a vast search space [9], to effectively reduce this space, the algorithm combines trained NN and an evolutionary approach.