Papers by Dmitriy Tarkhov
Communications in Computer and Information Science, 2021
Bookmarks Related papers MentionsView impact
Proceedings of the 2nd International Scientific Conference on Innovations in Digital Economy: SPBPU IDE-2020, 2020
Digital twins are one of the key technologies behind the Fourth Industrial Revolution. In the com... more Digital twins are one of the key technologies behind the Fourth Industrial Revolution. In the coming years they will be introduced on a large scale in the industry and in other spheres. A wide range of digital twins will be in demand: from separate components to complex technical facilities, such as automobiles, airplanes, manufacturing lines, factories, corporations, etc. To provide their successful interaction, it is important to create digital twins on the uniform principles. Currently, creating a digital twin is a complex scientific issue. It presents difficulties because it is necessary not only to describe physical (or chemical, biological, etc.) processes going on in the object, but also to envisage significant changes of its properties in the course of its operation. In this case the digital twin is supposed to adapt to the changes in the original object in accordance with the data received from the sensors. The aim of the research was to define the strategies of solving the current problems in such areas as digital twins, the internet of things and cyberphysical systems. In order to achieve this aim, the following problems were supposed to be solved: - Consider the definitions of the digital twin suggested in the world scientific literature - Find a unified data-driven real-time approach to creating digital twins - Suggest using the neural network approach in creating digital twins. During the use of the modelled object, specifics of the physical processes going on in it and object properties can change. The model is supposed to adapt in accordance with these changes, which is rather difficult if a model is generated by applying computer-aided engineering software packages (CAE) based on classical numerical methods. We consider the multistage technique as more promising. It involves building an adaptive model at the second stage. Such a model can be specified and redesigned based on real-time data. Since neural networks have proved to be efficient in solving complicated problems related to data processing, we recommend using them as the basic class of mathematical models for creating digital twins.
Bookmarks Related papers MentionsView impact
Semi-Empirical Neural Network Modeling and Digital Twins Development, 2020
Abstract In Chapter 1, we considered the first stage of the unified process of constructing a sem... more Abstract In Chapter 1, we considered the first stage of the unified process of constructing a semi-empirical neural network model of a real object, namely the construction of a functional characterizing the quality of the model. The next step of the unified process is to select the functional basis on which the solution should be based. In this chapter, we analyze a set of functional bases and neural network architectures from a single point of view and in uniform designations. Based on our experience, these specified bases are considered to be the most useful in our approach to the solution of ordinary differential equations and partial differential equations. Based on our experience, we have formulated recommendations for choosing the type of basis depending on the characteristics of the problem solved. In subdomains having simple geometry in the one-dimensional case, a fast and simple solution to the problem can be obtained using triangular basis functions, splines of the second or third order. If it is necessary to get a smooth solution, it is advisable to use the Gauss or Cauchy functions, and the calculations will be performed more slowly. In two-dimensional problems or problems of higher dimension, it is reasonable to use two-dimensional or multidimensional Gauss functions. In subdomains with pronounced anisotropy, it is possible to use ellipsoidal Gauss or Cauchy functions. In problems with a free boundary or in boundary control problems, when initially the domain boundary or parts of the section are not specified, but they are found in the process of solving the problem; we also used neural network expansions to describe them. To search for unknown boundaries, for example, separating different media or determining the shock wave, the functions of the perceptron type were the most promising.
Bookmarks Related papers MentionsView impact
Proceedings of the 2nd International Scientific Conference on Innovations in Digital Economy: SPBPU IDE-2020, 2020
When solving the problem of predicting impaired autoregulation of blood circulation in the brain,... more When solving the problem of predicting impaired autoregulation of blood circulation in the brain, scientists usually use a prognostic expression that interconnects the function of coherence of blood flow velocities in the arteries and atrerial pressure with a phase shift in the M-wave range. In our study we proposed to employ neural networks to adapt the method to specific patients or to a group of patients. A neural network algorithm has been developed to identify in the statistical properties of coherent biological signals present in a mixture with other signals and interference. The algorithm includes real-time determination of the coherence function of signals between fluctuations in systemic blood pressure and blood flow velocities in the left and right middle cerebral arteries and the phase shift function between these signals in the Mayer wavelength range. To reduce the influence of noise, it is proposed to use the technique of a sliding frame, divided into windows. The coherence and phase shift functions obtained in the windows are averagedwithin the frame boundaries. As a result, smoothed functions can be obtained in the time-frequency domain. To detect infractions of the cerebral autoregulation process, it is proposed to use trained neural feedforward network, which generalizing property can be improved as new experimental data are obtained while maintaining a balance between individual and general characteristics of patients.
Bookmarks Related papers MentionsView impact
After the problem formulation in the form of functional optimization and choosing the type of bas... more After the problem formulation in the form of functional optimization and choosing the type of basis functions, it is necessary to select an algorithm for finding the decomposition coefficients of the approximate neural network solution to the problem (1.1) according to the basis chosen and the method of the neural network restructuring. If it is necessary, the type of elements of the basis can also be fitted. The network structure justification implies the choice of the basis elements, the number of layers, and the number of elements in every layer. The selected algorithms should allow efficient parallel and distributed implementation. In this chapter, we create a complex of methods and algorithms for finding neural network dependence y = f(x, w) according to heterogeneous data. We suppose this data can be specified, using differential equations or other relationships. We focus on finding the structure of the function f in conjunction with searching the weight vector w. In the overw...
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Journal of Physics: Conference Series, 2020
High Intensity Focused Ultrasound (HIFU) is widely used in modern medicine. One of the important ... more High Intensity Focused Ultrasound (HIFU) is widely used in modern medicine. One of the important applications is the ablation of internal organ tumors under the HIFU heating. During this procedure, it is necessary to monitor the temperature in healthy adjacent tissues. Ultrasound thermometry (UST) is a promising non-invasive method of temperature control. The paper presents implementation of the UST technique in case of short-term local heating. A new algorithm suggested for ultrasound data processing improves the accuracy of the ultrasound thermometry technique to 2 °C.
Bookmarks Related papers MentionsView impact
Advances in Neural Networks – ISNN 2019, 2019
Focused ultrasound-based methods are widely used in various areas of medicine for vascular damage... more Focused ultrasound-based methods are widely used in various areas of medicine for vascular damage coagulation in limbs and internal organs, venous obliteration, and ablation of breast and thyroid tumors. To plan heat exposure and control its effectiveness, it is necessary to monitor temperature during the treatment procedure. The article proposes two technologies for such monitoring, namely infrared thermography and ultrasound thermometry using neural network methods.
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
In this chapter, we begin a detailed presentation of our approach to the construction of neural n... more In this chapter, we begin a detailed presentation of our approach to the construction of neural network models on heterogeneous information, including differential equations, boundary, initial and other conditions, measurement data, etc. The first stage of our approach consists in the transition from the given information to the functional, which numerically characterizes the correspondence of the model to the available information about the simulated object. We described this stage in the first chapter, both in general form and by many specific examples. We have shown a large number of examples so that the reader can find an example that is most suitable for his task and make the necessary modifications to the functional we have considered. As examples, we considered both problems for ordinary differential equations and problems for partial differential equations, both simple problems and problems having complicating features. The problems with parameters, stiff, differential-algeb...
Bookmarks Related papers MentionsView impact
В данной работе исследовано влияние температуры на механические характеристики при растяжении упр... more В данной работе исследовано влияние температуры на механические характеристики при растяжении упругого материала при помощи нейронных сетей. Для построения математических моделей использовались персептроны с различным числом нейронов. Оптимальные структура и веса нейронных сетей подбирались по экспериментальным данным с помощью метода наименьших квадратов. В процессе построения тестировались различные функции активации. Наилучший результат был получен при использовании функции активации сигмоидного типа. Образцами были выбраны высокопрочные термостойкие комплексные нити. Испытания проводились при 5-и различных уровнях температуры. На основе полученных данных была выявлена зависимость каждого из параметров от температуры материала. Также нейросетевая модель строилась по измерениям для данных нитей в ситуации со ступенчатым повышением температуры. Подобные эксперименты проводятся для ускорения процесса испытаний. Нейросетевая модель, построенная по части выборки, позволила построить д...
Bookmarks Related papers MentionsView impact
Данная статья продолжает исследования авторов по методам построения многослойных приближённых реш... more Данная статья продолжает исследования авторов по методам построения многослойных приближённых решений дифференциальных уравнений в виде функций. Эти методы основаны на применении классических формул приближённого решения дифференциальных уравнений к интервалу с переменным верхним пределом. Они успешно применялись авторами при решении задач для обыкновенных дифференциальных уравнений. Решение начально-краевых задач для уравнений в частных производных наталкивается на определенные сложности. Мы тестируем предлагаемые способы преодоления этих сложностей в первую очередь на простых задачах, имеющих известное аналитическое решение. Здесь мы рассматриваем задачу для простейшего волнового уравнения с одной пространственной переменной в случае специальных начальных условий (Гауссиан) и нулевых краевых условий на бесконечности. Мы сравниваем различные методы на основе вычислительных экспериментов: метод Эйлера, исправленный метод Эйлера, метод Штёрмера и его модификации. Результаты применени...
Bookmarks Related papers MentionsView impact
The construction of multilayer approximate solutions of differential equations based on classical... more The construction of multilayer approximate solutions of differential equations based on classical numerical methods is used to approximate special functions as solutions of the corresponding differential equations. In this paper, we investigate the Bessel equation. Multilayer methods were introduced by the authors earlier as a way to construct approximate solutions in an analytical form similar to deep learning neural networks without the need, but with the possibility of such training. The problem of approximating Bessel functions is considered classical, but it remains relevant due to the requirements of modern physics and related calculations. In this paper, we construct unified parametric approximate solutions for Bessel functions of different orders and give examples of specific approximations for negative and positive orders of Bessel functions of the first kind, including for half-integer values. Both explicit and implicit methods are considered as basic methods for construct...
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Advances in Neural Computation, Machine Learning, and Cognitive Research, 2017
A new approach to the construction of multilayer neural network approximate solutions for evoluti... more A new approach to the construction of multilayer neural network approximate solutions for evolutionary partial differential equations is considered. The approach is based on the application of the recurrence relations of the Euler, Runge-Kutta, etc. methods to variable length intervals. The resulting neural-like structure can be considered as a generalization of a feedforward multilayer network or a recurrent Hopfield network. This analogy makes it possible to apply known methods to the refinement of the obtained solution, for example, the backpropagation algorithm. Earlier, a similar approach has been successfully used by the authors in the case of ordinary differential equations. Computational experiments are performed on one test problem for the one-dimensional (in terms of spatial variables) heat equation. Explicit formulas are derived for the dependence of the resulting neural network output on the number of layers. It was found that the error tends to zero with an increasing number of layers, even without the use of the network learning.
Bookmarks Related papers MentionsView impact
Thermal Science, 2019
In this paper, we conduct the comparative analysis of two neural network approaches to the proble... more In this paper, we conduct the comparative analysis of two neural network approaches to the problem of constructing approximate neural network solutions of non-linear differential equations. The first approach is connected with building a neural network with one hidden layer by minimization of an error functional with regeneration of test points. The second approach is based on a new continuous analog of the shooting method. In the first step of the second method, we apply our modification of the corrected Euler method, and in the second and subsequent steps, we apply our modification of the St?rmer method. We have tested our methods on a boundary value problem for an ODE which describes the processes in the chemical reactor. These methods allowed us to obtain simple formulas for the approximate solution of the problem, but the problem is special because it is highly non-linear and also has ambiguous solutions and vanishing solutions if we change the parameter value.
Bookmarks Related papers MentionsView impact
Journal of Physics: Conference Series, 2018
Bookmarks Related papers MentionsView impact
Journal of Physics: Conference Series, 2018
Bookmarks Related papers MentionsView impact
MATEC Web of Conferences, 2018
Bookmarks Related papers MentionsView impact
MATEC Web of Conferences, 2018
The critical review presents an analysis of foreign studies designed to assess the state of worki... more The critical review presents an analysis of foreign studies designed to assess the state of working conditions. The aim of the work is to identify the main areas of research that can be adapted for Russian enterprises. It was found that there are several foreign instruments for assessing the state of working conditions, on the basis of which a new methodology applicable to Russian enterprises can be formed, which will greatly contribute to the prevention of accidents at the workplace.
Bookmarks Related papers MentionsView impact
Uploads
Papers by Dmitriy Tarkhov