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The neural network predicts stable crystal structures

Weike Ye et al. / Nature Communications

Scientists from the United States have developed a neural network that calculates the binding energy of crystals with an error of the order of 10 millielectronvolts per atom, but does not require large computational resources. Such a low error is sufficient to estimate the stability of potentially useful materials predicted theoretically. In addition, the researchers launched an online service that calculates the binding energy of garnets using the developed program. The article is published in  Nature Communications .

Scientists constantly predict new materials with unusual properties, but not all such predictions can be realized in practice. To prove that the invented structure is really viable, it is necessary to assess its stability, and such an assessment is one of the main tasks of materials science . At present, scientists are able to assess the stability of materials in two fundamentally different ways. On the one hand, they can use “chemical intuition” – Pauling’ssemi-empirical rules that describe at what parameters of ions and lattice the crystal will remain stable. On the other hand, researchers can calculate the binding energy of the crystal atoms “from the first principles” (usingmethod DFT ) and directly check how it will be stable.

At first glance, it seems that the second method is more convenient, since it makes it possible to determine the stability of completely arbitrary lattices and relies only on the fundamental laws of quantum mechanics. Nevertheless, it has a big drawback: quantum-mechanical calculations require a lot of resources, and therefore they can be carried out only with the help of a supercomputer. Therefore, in order to calculate the stability of the next structure, you have to pay for the computational time and wait until the supercomputer is freed. It’s expensive and uncomfortable. To solve this problem, scientists suggested using machine learning, a method in which the program adapts to the problem being solved (for example, it highlights the parameters that most influence the final result). More information about this method can be found in the material”ABC of AI:” Machine learning ” . Unfortunately, so far scientists have not been able to bring the accuracy of calculations to such a level that they could be used to evaluate the stability of the material. In fact, most self-learning programs calculate the binding energy of crystal atoms with an error of the order of 100 millielectronvolts, while 90 percent of known crystals have a binding energy of less than 70 millielectronvolts per atom.

A group of scientists led by Shyue Ping Ong developed a program that calculates the binding energy of a crystal with an accuracy of about 10 millielectronvolts per atom, but does not require large computational resources. To do this, scientists built a neural network of direct propagation(feed-dorward neural network) and suggested that basically the binding energy of the atoms of the crystal determines only two parameters – the sizeand  electronegativity of the crystal ions. On this assumption, scholars pushed the rules of Pauling. More information about neural networks can be found in our material from the series “ABC of Artificial Intelligence” . To train the neural network, researchers used a databaseabout the crystal structure and the binding energy of 635  garnets . These scientists randomly divided the data in a ratio of 64:16:20 and then sent them to the training, confirmation and verification of the work of the neural network, respectively.

The first trial version of the neural network had one hidden layer , worked only with the specified parameters and predicted the binding energy of the crystal only on the basis of its chemical composition, not taking into account the crystal structure. Accuracy was calculated energy of about 25 meV atom, which is almost two times smaller than the error of other self-learning programs, but still does not reach the “fair” DFT calculations using the method. This indicates that the scientists’ guess was correct, and the binding energy is mainly determined by only two parameters.

Then the researchers built a second version of the neural network, which took into account not only the radius and electronegativity of the ions, but also the structure of the unit cell of the garnet. In addition, this time the neural network had already two hidden layers. After training the program on the same sample, the scientists found that this time the error was only 10 millielektronvolt per atom. Such a low error makes it possible to evaluate the stability of materials – according to scientists, their program correctly predicts whether the crystal will be stable or not, in 90 percent of cases.

Finally, scientists used the same approach to calculate the binding energy and evaluate the stability of perovskites  – compounds whose crystal structure differs from the structure of garnets. In this case, the calculation error was approximately 20 millielectrovolt per atom. Interestingly, in parallel with the article of the Onga group, another article appeared in which the binding energy of perovskites is estimated using the kernel ridge regression model and has a comparable error. Nevertheless, in this article the researchers used 70 parameters instead of two, which complicated the calculations.

The authors of the article believe that their work is of practical importance, since garnets and perovskites are used to create solar cells, LEDs and batteries. Therefore, scientists launched an online service , which on the fly calculates the energy of the connection of garnets with the help of the developed program. Thanks to this service, researchers will no longer have to resort to supercomputers to assess the viability of new potentially useful compounds.

Recently, scientists are increasingly using machine learning to find new materials with unusual properties and to understand how individual molecules of matter interact with each other. For example, in October 2017, researchers from the United States and Germany calculated with the help of a neural network the electron density of molecules, and then on the basis of these calculations explained the chemical properties of the relevant substances. In April of this year, scientists from Great Britain and Japan learned how to quickly find the potential of interaction of boron atoms in crystalline structures, forcing the program to be trained on the fly. In the same month, physicists from the UK and Finland showedwith the help of machine learning, how to form amorphous carbon films with a high content of tetrahedral carbon. We also wrote about how physicists use neural networks to calculate functional integrals and  topological invariants of one-dimensional systems.

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