Rubric: "1.2.2. Mathematical modeling, numerical methods and software packages (technical sciences)"
519.6 Agent model of two competing populations taking into account their structurality
Belotelov N. V. (Bauman Moscow State Technical University/Institution of Russian Academy of Sciences Dorodnicyn Computing Centre of RAS), Brovko A. V. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2022-3-7183
The article describes an agent simulation model of two populations competing for one resource. In the model, it is assumed that an individual dies if its mass-energy becomes non-positive. It is assumed that individuals of each of the populations under consideration can form flocks, this allows populations to increase their competitiveness. In the model, this is formalized through the ability to organize networks connecting individuals of the same species. At the same time, individuals can form only a certain number of connections with neighbors. The concept of "valence" is introduced in the model to describe this. It is assumed that within each network there is an instantaneous redistribution of the resource available to all members of the network by each member of the pack. In addition to the model, the article describes the structure of the program with which simulation experiments were carried out. As a result of the simulation experiments, the following was obtained. If the resource is highly productive, then in the process of competitive interaction, the population wins, the agents of which have a large "valence". And in the case of a low-productive resource, individuals of a population with a lower "valence" win in competitive interaction. This is due to the fact that more complex structures require more energy to maintain the flock.
Белотелов Н.В., Бровко А.В. Агентная модель двух конкурирующих популяций с учетом их структурности. Математическое моделирование и численные методы, 2022, № 3, с. 71–83.
004.855.5 Neural network methods for solving the problem of credit scoring
Kadiev A. D. (Bauman Moscow State Technical University), Chibisova A. V. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2022-4-8192
The mathematical derivation of the presented neural network model is demonstrated. Reduction of the classification problem to an optimization problem. Produced recon-naissance data analysis, as well as their preprocessing for further use in training classification algorithms. The architectures of neural networks were designed depending on the activation function, the number of hidden layers of the neural network and the number of neurons in the hidden layers. More than ten neural networks were trained to solve the task of credit scoring. The calculation of the learning time of neural networks was made. The solution of the problem using classical machine learning algorithms is presented. It could be seen that the standard deviation of accuracy and ROC AUC for neural networks is greater than that of a random forest. This is due to the fact that we choose the initial weights randomly and calculate the gradients not on the entire sample, but on small parts, which adds some learning error. But these deviations were not only for the worse. In the best situations, according to both metrics, neural networks showed the worst result by a couple of percent. The analysis of results is made. Comparative analysis shows that neural networks have better classification quality than classical machine learning algorithms, and also that neural networks have less training time than classical machine learning algorithms. Graphs and tables displaying the results obtained are presented.
Кадиев А.Д., Чибисова А.В. Нейросетевые методы решения задачи кредитного скоринга. Математическое моделирование и численные методы, 2022, № 4, с. 81–92.
Isaev V. I. (Khristianovich Institute of Theoretical and Applied Mechanics SB RAS), Cherepanov A. N. (Khristianovich Institute of Theoretical and Applied Mechanics SB RAS), Shapeev V. P. (Khristianovich Institute of Theoretical and Applied Mechanics SB RAS/Новосибирский государственный университет)
doi: 10.18698/2309-3684-2023-1-8191
We proposed a self-consistent thermokinetic model of binary alloy crystallization in the weld joint modified by nanodimensional inoculators added to the welding pool during the laser weling process. This combined model of laser welding of uniform metals describes thermophysical prcesses of macroscopic properties of the weld joint and its structure depending on welding regimes and properties of nanomodifying powders (capillary angle, powder concentration). It is based on a thermophysical model of the action of the laser radiation on metal during the laser welding of metallic plates. The simulation is supplemented with a nonequilibrium model of heerogeneous nucleation and the growth of crystalline phase on nanomodifying particles added to the welding pool during the cooling and solidification of alloy in the weld joint. Numerical simulations based on the collocations and least squared methods were performed for butt weling of plates made of a binary aluminum alloy. We calculated the temperature distribution in the plates, the shape of the cross-section of the welding pool, and quantitative properties of its crystal structure. We investigated the effect of the capillary angle and nanomodifying powder concentration on the crystal grain size
Исаев В.И., Черепанов А.Н., Шапеев В.П. Исследование влияния смачиваемости и концентрации модифицирующих наночастиц на структуру шва при лазерной сварке алюминиевого сплава. Математическое моделирование и численные методы, 2023, No 1, с. 81–91.
Andrushchenko V. A. (Institute for Computer Aided Design of the Russian Academy of Sciences), Syzranova N. G. (Institute for Computer Aided Design of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2023-3-4261
Within the framework of the actual problem of comet-asteroid danger, the physical processes that cause the destruction and fragmentation of meteoric bodies in the Earth's atmosphere, in this case the Tunguska bolide, are numerically studied. The number of possible versions and hypotheses related to the Tunguska phenomenon is extremely large and continues to increase, therefore, an analysis and generalization of all known facts inherent in this non-standard catastrophic event is necessary, and only then proceed to the nomination of certain hypotheses explaining it. Based on the developed physical and mathematical model that determines the movement of space objects of natural origin in the atmosphere and their interaction with it, we have proposed two hypotheses explaining the processes occurring during the fall of the Tunguska body in 1908. The first hypothesis is related to the fragmentation of the body, which is a stone meteoroid into a large number of fragments, which collapsed in the dense layers of the atmosphere under the action of thermal stresses to the size of fine dust. The difficulties in identifying small particles that fell out as a result of the Tunguska event are mainly explained by the following circumstance: the timing of the initial search for traces of the fall of the body was removed from the moment of the event by as much as twenty years, during which a very significant number of other geophysical processes could occur in this area. The second hypothesis is related to phenomena that occur at small angles of entry of a body into the Earth's atmosphere. In this case, there is a change in the ballistics of its flight in the atmosphere, consisting in a transition from the fall mode to the ascent mode. This effect leads to the realization of the following possible scenarios of the event: the return of the body back to outer space at its residual velocity greater than the second cosmic one; the transition of the body to the orbit of the Earth satellite at a residual velocity greater than the first cosmic one; at lower values of the residual velocity of the body, its return after some time to the fall mode and reaching the earth's surface at a considerable distance from the intended crash site. The proposed hypotheses explain, for example, the absence of material traces, including craters, during the search for the remains of the Tunguska bolide in the vicinity of the forest collapse.
Андрущенко В.А., Сызранова Н.Г. Моделирование Тунгусского явления 1908 года в рамках двух возможных гипотез. Математическое моделирование и численные методы, 2023, № 3, с. 42–61.
519.6 Agent-based model of cultural interactions on non-metrizable Hausdorff spaces
Belotelov N. V. (Bauman Moscow State Technical University/Institution of Russian Academy of Sciences Dorodnicyn Computing Centre of RAS), Pavlov S. A. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2021-3-105119
The need to develop formalized computer-oriented approaches to conducting interdisciplinary research of intercultural interactions is an urgent task. The article describes an approach to the development of agent models of intercultural interactions based on the use of non-metrizable Hausdorff spaces using genetic algorithms to introduce dynamic changes in the structure of cultural agents under consideration. The article considers a prototype of an agent model in which the state of agents is described in Hausdorff spaces. Using the choice of reference points for each agent, the Uryson function is built, which allows you to enter the preferences of agents. Further, using the technology of gentic algorithms, it is possible to obtain the clock dynamics of changes in the entire system of agents. The article describes some simulation experiments. Possible prospects for the development of this approach are discussed.
Белотелов Н.В, Павлов С.А. Агентная модель культурных взаимодействий на неметризуемых хаусдорфовых пространствах. Математическое моделирование и численные методы, 2021, № 3, с. 105–119.
Bushuev A. Y. (Bauman Moscow State Technical University), Danilov N. A. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2022-2-313
A mathematical model of functioning of synchronization systems of actuators based on a throttle flow divider was developed to solve design problem. The solution of the optimization problem of a mismatch time of movement of actuators operating under conditions of external alternating-sign force effects is given, performed using the genetic algorithm and refined using the Nelder-Mead algorithm
Бушуев А.Ю., Данилов Н.А. Математическое моделирование гидравлической системы синхронизации исполнительных органов на основе дроссельного делителя потока. Математическое моделирование и численные методы, 2022, № 2, с. 3–15
519.63 Modification of aluminum by laser shock wave detected in atomistic modeling
Perov E. A. (JIHT), Zhakhovsky V. V. (Dukhov Automatics Research Institute/JIHT), Алимович N. A. (L.D. Landau Institute for Theoretical Physics RAS), Shepelev V. V. (Institute for Computer Aided Design of the Russian Academy of Sciences), Fortova S. V. (Institute for Computer Aided Design of the Russian Academy of Sciences), Doludenko A. N. (JIHT)
doi: 10.18698/2309-3684-2023-4-7492
Plastic deformations are the basis of such industrial technology as laser thermal hardening or laser pinning (LSP, laser shock peening). In this paper, the possibility of hardening the surface layer of an aluminum sample irradiated by a single femtosecond laser pulse is investigated by the method of classical molecular dynamics. Several initialstates of the film are simulated; three orientations of the crystal lattice are investigated — [1, 0, 0] (the first orientation of the crystal lattice), [1, 1, 0] (the second orientation of the crystal lattice), [1, 1, 1] (the third orientation of the crystal lattice). A numerical study of the effect of various values of the invested energy in the range from 120,98 J/m2 to 2540,01 J/m2 of a laser pulse on the depth of plastic deformations affecting the hardening of the material under study was carried out. The energy values were selected in such a way that the plastic front of the UV (shock wave) stopped before it reached the right boundary of the simulated film. If this condition is not observed, then the dependence cannot be considered correctly constructed, since the stretching wave reflected from the right boundary of the sample will slow down the plastic shock front, acting as an unloading wave. With the help of this dependence, the threshold value of the invested energy is determined, when exceeded, aluminum begins to deform plastically.
Перов E.А., Жаховский В.В., Иногамов Н.А., Шепелев В.В., Фортова С.В., Долуденко А.Н.. Молекулярно-динамическое моделирование модификации алюминия лазерной ударной волной. Математическое моделирование и численные методы, 2023, № 4, с. 74-92
519.6 Numerical solution of equations of mixed type in unlimited region on a plane
Galanin M. P. (Bauman Moscow State Technical University/Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes), Ukhova A. R. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2023-3-105124
The purpose of the work is to build and implement an algorithm for finding a numerical solution to a problem for mixed-type equations in an unlimited region. In this case problems are considered in which the process under study is described in some limited area by the thermal conductivity equation or wave equation, and outside it by the Laplace equation. The necessary additional conditions at zero, at infinity and the conditions for conjunction at the border of the inner region are set. There is described an algorithm for finding a numerical solution to a problem with a wave equation in a limited region in one-dimensional and two-dimensional cases, problems with a thermal conductivity equation or a wave equation in a two-dimensional case. Difference schemes are built by the integro–interpolation method. The task is solved in a limited area. Nonlocal boundary conditions are set on its border so the solution of task in limited area coincides with projection of problem in unlimited area. In this case, an artificial boundary is introduced for the solution in the part of the region in which the process is described by the Laplace equation. An iterative algorithm and an algorithm with a non-local boundary condition are built. The results of calculations for examples in various fields are presented.
Галанин М.П., Ухова А.Р. Численное решение уравнений смешанного типа в неограниченной области на плоскости. Математическое моделирование и численные методы, 2023, № 3, с. 105–124.
Mozzhorina T. Y. (Bauman Moscow State Technical University), Rakhmankulov D. A. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2021-3-7487
In this paper, the optimization of the transfer of a low–mass satellite from the Earth's orbit to the Mars orbit under a solar sail is considered. Optimization of the control of the pitch angle of the solar sail is carried out using the Pontryagin maximum principle while minimizing the flight time. In contrast to previous works on this topic, the solution of the boundary value problem, to the solution of which the maximum principle is reduced, was obtained by the false position method. The calculation program is written in the C++ programming language. Despite the computational difficulties arising when using the false position method, it was possible to achieve good convergence of the Newton method underlying the algorithm. The analysis of the accuracy of the results obtained is carried out and the possibility of using the false position method in solving such problems is shown. A comparison is made with the data of previously published works. Despite some assumptions used in the development of the calculation algorithm, the work has its value in terms of assessing the possibility of using the false position method, which gives the most accurate numerical optimization results.
Мозжорина Т.Ю., Рахманкулов Д.А. Моделирование и оптимизация управлением спутника малой массы при перелете с орбиты Земли на орбиту Марса под солнечным парусом. Математическое моделирование и численные методы, 2021, № 3, с. 74–87.