Our main motivation is to propose an efficient approach to generate novel multi-element stable chemical compounds that can be used in real world applications. This task can be formulated as a combinatorial problem, and it takes many hours of human experts to construct, and to evaluate new data. Unsupervised learning methods such as Generative Adversarial Networks (GANs) can be efficiently used to produce new data.   Cross-domain Generative Adversarial Networks were reported to achieve exciting results in image processing applications. However, in the domain of materials science, there is a need to synthesize data with higher order complexity compared to observed samples, and the state-of-the-art cross-domain GANs can not be adapted directly. 

 In this contribution, we propose a novel GAN called CrystalGAN which generates new chemically stable crystallographic structures with increased domain complexity. We introduce an original architecture, we provide the corresponding loss functions, and we show that the CrystalGAN generates very reasonable data. We illustrate the efficiency of the proposed method on a real original problem of novel hydrides discovery that can be further used in development of hydrogen storage materials. In modern society, a big variety of inorganic compositions are used for hydrogen storage owing to its favorable cost BID4 . A vast number of organic molecules are applied in solar cells, organic light-emitting diodes, conductors, and sensors BID25 . Synthesis of new organic and inorganic compounds is a challenge in physics, chemistry and in materials science. Design of new structures aims to find the best solution in a big chemical space, and it is in fact a combinatorial optimization problem.In this work, we focus on applications of hydrogen storage, and in particular, we challenge the problem to investigate novel chemical compositions with stable crystals. Traditionally, density functional theory (DFT) plays a central role in prediction of chemically relevant compositions with stable crystals BID22 . However, the DFT calculations are computationally expensive, and it is not acceptable to apply it to test all possible randomly generated structures.A number of machine learning approaches were proposed to facilitate the search for novel stable compositions BID3 . There was an attempt to find new compositions using an inorganic crystal structure database, and to estimate the probabilities of new candidates based on compositional similarities. These methods to generate relevant chemical compositions are based on recommender systems BID10 . The output of the recommender systems applied in the crystallographic field is a rating or preference for a structure. A recent approach based on a combination of machine learning methods and the high-throughput DFT calculations allowed to explore ternary chemical compounds BID21 , and it was shown that statistical methods can be of a big help to identify stable structures, and that they do it much faster than standard methods. Recently, support vector machines were tested to predict crystal structures BID16 showing that the method can reliably predict the crystal structure given its composition. It is worth mentioning that data representation of observations to be passed to a learner, is critical, and data representations which are the most suitable for learning algorithms, are not necessarily scientifically intuitive BID23 .Deep learning methods were reported to learn rich hierarchical models over all kind of data, and the GANs BID8 ) is a state-of-the-art model to synthesize data. Moreover , deep networks were reported to learn transferable representations BID18 . The GANs were already exploited with success in cross-domain learning applications for image processing BID13 BID12 .Our goal is to develop a competitive approach to identify stable ternary chemical compounds, i.e., compounds containing three different elements, from observations of binary compounds. Nowadays , there does not exist any approach that can be applied directly to such an important task of materials science. The state-of-the-art GANs are limited in the sense that they do not generate samples in domains with increased complexity, e.g., the application where we aim to construct crystals with three elements from observations containing two chemical elements only. An attempt to learn many-to-many mappings was recently introduced by BID0 , however, this promising approach does not allow to generate data of a higher-order dimension.Our contribution is multi-fold:• To our knowledge, we are the first to introduce a GAN to solve the scientific problem of discovery of novel crystal structures, and we introduce an original methodology to generate new stable chemical compositions; • The proposed method is called CrystalGAN, and it consists of two cross-domain GAN blocks with constraints integrating prior knowledge including a feature transfer step; • The proposed model generates data with increased complexity with respect to observed samples; • We demonstrate by numerical experiments on a real challenge of chemistry and materials science that our approach is competitive compared to existing methods; • The proposed algorithm is efficiently implemented in Python, and it will be publicly available shortly, as soon as the contribution is de-anonymized.This paper is organized as follows. We discuss the related work in Section 2. In Section 3, we provide the formalisation of the problem, and introduce the CrystalGAN. The results of our numerical experiments are discussed in Section 4. Concluding remarks and perspectives close the paper. In our numerical experiments, we compare the proposed CrystalGAN with a classical GAN, the DiscoGAN BID13 , and the CrystalGAN but without the geometric constraints. All these GANs generate POSCAR files, and we evaluate the performance of the models by the number of generated ternary structures which satisfy the geometric crystallographic environment. Table 2 shows the number of successes for the considered methods. The classical GAN which takes Gaussian noise as an input, does not generate acceptable chemical structures. The DiscoGAN approach performs quite well if we use it to generate novel pseudo-binary structures, however, it is not adapted to synthesize ternary compositions. We observed that the CrystalGAN (with the geometric constraints) outperforms all tested methods.From multiple discussions with experts in materials science and chemistry, first, we know that the number of novel stable compounds can not be very high, and it is already considered as a success if we synthesize several stable structures which satisfy the constraints. Hence, we can not really reason in terms of accuracy or error rate which are widely used metrics in machine learning and data mining.Second, evaluation of a stable structure is not straightforward. Given a new composition, only the result of density functional theory (DFT) calculations can provide a conclusion whether this composition is stable enough, and whether it can be used in practice. However, the DFT calculations are computationally too expensive, and it is out of question to run them on all data we generated using the CrystalGAN. It is planned to run the DFT calculations on some pre-selected generated ternary compositions to take a final decision on practical utility of the chemical compounds. Our goal was to develop a principled approach to generate new ternary stable crystallographic structures from observed binary, i.e. containing two chemical elements only. We propose a learning method called CrystalGAN to discover cross-domain relations in real data, and to generate novel structures. The proposed approach can efficiently integrate, in form of constraints, prior knowledge provided by human experts.CrystalGAN is the first GAN developed to generate scientific data in the field of materials science. To our knowledge, it is also the first approach which generates data of a higher-order complexity, i.e., ternary structures where the domains are well-separated from observed binary compounds. The CrystalGAN was, in particular, successfully tested to tackle the challenge to discover new materials for hydrogen storage.Currently, we investigate different GANs architectures, also including elements of reinforcement learning, to produce data even of a higher complexity, e.g., compounds containing four or five chemical elements. Note that although the CrystalGAN was developed and tested for applications in materials science, it is a general method where the constraints can be easily adapted to any scientific problem.
"Generating new chemical materials using novel cross-domain GANs."
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