MACHINE LEARNING METHODS FOR QUANTUM CHEMISTRY PROBLEM

МЕТОДЫ МАШИННОГО ОБУЧЕНИЯ В ЗАДАЧАХ КВАНТОВОЙ ХИМИИ

Степанов Игорь Владимирович,

магистрант, Самарский государственный медицинский университет,

РФ, г. Самара

Рябов Николай Анатольевич,

научный руководитель, канд. фарм. наук, старший научный сотрудник НИИ «БиоТех»,

РФ, г. Самара

ABSTRACT

Currently, atomistic modeling has become a necessary tool in problemsoptimization of ligand-protein interactions for the creation of new drugs and the search for newmaterials for energy. The methods of quantum mechanics underlying the modeling allow. It is sufficient to accurately calculate the properties of organic and inorganic compounds. However, the usual. Traditional methods of quantum mechanics are quite complex to use due to their computational complexity and the necessary calculations for industry can take hours, days, weeks, which significantly hinders technological progress. The solution is to use machine learning methods based on the description systems in terms of quantum mechanics. These methods significantly speed up the calculation industrially relevant properties of various compounds and at the same time improve the quality of assessment these properties compared to existing methods. This work will describe advantages of machine learning methods in atomistic modeling for industrial research problems.

АННОТАЦИЯ

В настоящее время атомистическое моделирование стало необходимым инструментом в задачах оптимизации взаимодействия лиганд-белок для создания новых лекарственных средств и поиска новых материалов для энергетики. Лежащие в основе моделирования методы квантовой механики, позволяют достаточно точно вычислять свойства органических и неорганических соединений. Однако, обычные, традиционные методы квантовой механики достаточно сложны для использования в связи со своей вычислительной сложностью и необходимые расчеты для промышленности могут занимать часы, дни, недели, что значительно сдерживает технологических прогресс. Решением является использование методов машинного обучения, основывающихся на описании системы в терминах квантовой механики. Данные методы значительно ускоряют вычисление промышленно значимых свойств различных соединений и в то же время повышают качество оценки этих свойств по сравнению с существующими методами. В данной работе будут описаны преимущества методов машинного обучения в атомистическом моделировании для исследовательских задач промышленности.

Keywords: machine learning, quantum chemistry, atomistic modeling, machine learning algorithms.

Ключевые слова: машинное обучение, квантовая химия, атомистическое моделирование, алгоритмы машинного обучения.

Description of the algorithm

The atomistic modeling process is a computational process for assessing the properties of substances ab initio, i.e. without conducting experiments. Atomistic modeling is based on the use of either (semi-)empirical interatomic potentials or quantum mechanical models of interatomic interaction. Models of the first group are computationally efficient, but the accuracy they obtain is sometimes insufficient. Models of the second group make it possible to obtain high accuracy, but are extremely expensive in terms of computational complexity. The methods of the second group are based on the fundamental idea of ​​density functional theory (DFT) [1]. The Kohn-Sham method is a standard method for theoretical studies of the electronic structure of materials. In this theory, the solution to the Kohn-Sham equation

with density n(r), calculated by summing |φi (r)| 2 for all occupied states, allows us to obtain the total energy of the system and the density distribution of the interacting electronic system under the ionic potential Vion. The exchange-correlation potential Vxc[n] is a density functional. There are well known materials for which an accurate DFT description has not yet been obtained. Also, some modern functionals have been criticized for biasing towards an accurate description of energy rather than density, despite the fact that both phenomena are significant. Next, we will consider the use of machine learning methods in the problem of predicting exchange-correlation potentials Vxc[n]. The first work on the application of machine learning methods to density functionals was carried out by Burke’s group [2, 3, 4], but in this work we can present the results of [1], where a team of authors proposes to use a neural network algorithm to predict Vxc. To build the neural network architecture shown in Figure 1, the authors used a multilayer perspetron, which has input features that describe various small molecules (water, ammonia, nitric oxide). These features are calculated based on the density n(r) and their complete mathematical properties are given in [1]. Using this method of machine learning, but not limited to it, you can obtain a significant acceleration of the calculations, which is extremely important for conducting a larger number of computational experiments without losing the quality of the prediction. However, it is important to remember that the correctly selected features by an expert or another algorithm, as well as the appropriate variety of training data, are the most important elements of the algorithm's learning process. Machine learning algorithms have an excellent ability to find the laws underlying the given data, but have problems associated with overfitting, which is reflected in poor generalization in the case of new data that may differ in the type of molecule, which is reflected in both structure and conformation of the molecule. One solution to this problem is such engineering of input features and such a change in the architecture of the neural network that could take into account various physical principles (symmetry, etc.) underlying the calculation of molecular potentials.

Figure 1. Neural network architecture

The main task of quantum chemistry is the approximate solution of the electronic Schrödinger equation. An exact analytical solution is no longer possible for a two-electron system and today enough a large number of methods for approximate solution of the Schrödinger equation. The “gold standard” for calculating the ground state energy, with the exception of highly correlated systems, is considered to be the connected cluster method, however it is quite demanding in terms of computing power.

The last few years have seen an exponential increase in the number of works dedicated to the application of machine learning techniques for approximate solutions to the Schrödinger equation. The main advantage of this method is its high performance; a trained neural network can predict the properties of large molecular systems in a time comparable to the time it takes to perform a molecular mechanical calculation. The purpose of this work was to study the capabilities of the neural network U-Net architecture, recently created at Stanford University. This the neural network was trained on the basis of only organic molecules based on the results of calculating the B3LYP density functional and further trained on several hundred CCSD/CCSD(T) calculations.

Only the electron density of the molecule, calculated by the Hartree-Fock method, and the output is a correction to the atomization energy and electron density. The objective of this work was to test the applicability of this neural network for predicting the properties of inorganic molecules. As a result, the neural network used in this work makes it possible to predict values of energies and electron densities even on inorganic molecules that were absent in the training set, including values on molecules containing elements that were not part of the molecules from the training series.

Conclusion

The paper describes an example of using the machine learning method to solve a quantum chemistry problem, namely a method based on the use of a neural network algorithm. The work does not mention specific computational results, comparisons with existing solutions, or further ways of developing the algorithm. These shortcomings will be eliminated in subsequent works on this topic.

References:

1. Nagai R. Completing density functional theory by machine learning hidden messages from molecules. Comput Mater. – 2020. – vol. 43.
2. Snyder J. C. Finding density functionals with machine learning. Phys. Rev. Lett. – 2012. – vol. 108.
3. Snyder J. C. Orbital-free bond breaking via machine learning. Chem. Phys. – 2013. – vol. 139.
4. Li L. Understanding machine-learned density functionals. Int. Quantum Chem. – 2016. – vol. 116. –.P. 819-833.