**and Communications Technologies 135**

### Zhengbing Hu Qingying Zhang Sergey Petoukhov Matthew He Editors

## Advances in Artificial Systems

## for Logistics

## Engineering

### and Communications Technologies

### Volume 135

Series Editor

Fatos Xhafa, Technical University of Catalonia, Barcelona, Spain

technologies and communications. It will publish latest advances on the engineering task of building and deploying distributed, scalable and reliable data infrastructures and communication systems.

The series will have a prominent applied focus on data technologies and communications with aim to promote the bridging from fundamental research on data science and networking to data engineering and communications that lead to industry products, business knowledge and standardisation.

Indexed by SCOPUS, INSPEC, EI Compendex.

All books published in the series are submitted for consideration in Web of Science.

More information about this series athttps://link.springer.com/bookseries/15362

### Sergey Petoukhov

^{•}

### Matthew He

### Editors

### Advances in Arti ﬁ cial Systems for Logistics Engineering

### 123

Zhengbing Hu

School of Computer Science Hubei University of Technology Wuhan, China

Sergey Petoukhov

Mechanical Engineering Research Institute of the Russian Academy of Sciences Moscow, Russia

Qingying Zhang

College of Transportation and Logistics Engineering

Wuhan University of Technology Wuhan, China

Matthew He

Halmos College of Arts and Sciences Nova Southeastern University Ft. Lauderdale, FL, USA

ISSN 2367-4512 ISSN 2367-4520 (electronic) Lecture Notes on Data Engineering and Communications Technologies ISBN 978-3-031-04808-1 ISBN 978-3-031-04809-8 (eBook) https://doi.org/10.1007/978-3-031-04809-8

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The development of artiﬁcial intelligence (AI) systems and their applications in variousﬁelds belongs to the most urgent tasks of modern science and technology.

One of these areas is AI and logistics engineering, in which their application is aimed at increasing the effectiveness of the generation and distribution of AI for the life support of the world’s population, including the tasks of developing industry, agriculture, medicine, transport, etc. The rapid development of AI systems requires the intensiﬁcation of training of a growing number of relevant specialists. AI systems also have a lot of potential for use in education technology to improve the quality of training for specialists, taking into account the personal characteristics of these specialists and the new computing devices that are coming out.

For these reasons, the Second International Conference on Artiﬁcial Intelligence and Logistics Engineering (ICAILE2022), held in Kyiv, Ukraine, on 20–22 February 2022, organized jointly by the National Technical University of Ukraine

“Igor Sikorsky Kyiv Polytechnic Institute”, Wuhan University of Technology, Nanning University, National Aviation University, and the International Research Association of Modern Education and Computer Science. The ICAILE2022 brings together leading scholars from all around the world to share their ﬁndings and discuss outstanding challenges in computer science, logistics engineering, and education applications.

The best contributions to the conference were selected by the programme committee for inclusion in this book out of all submissions.

Zhengbing Hu February 2022

Qingying Zhang Sergey Petoukhov Matthew He

v

### Conference Organizers and Supporters

National Technical University of Ukraine“Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine

Wuhan University of Technology, China Nanning University, China

National Aviation University, Ukraine

Huazhong University of Science and Technology, China Polish Operational and Systems Society, Poland

Wuhan Technology and Business University, China

International Research Association of Modern Education and Computer Science, Hong Kong

vii

Mathematical Advances in Schemes for Logistics Engineering Accelerating Simulation of the PDE Solution by the Structure

of the Convolutional Neural Network Modifying. . . 3 Valentyn Kuzmych and Mykhailo Novotarskyi

Combined Machine Learning Model for Covid-19 Analysis

and Forecasting in Ukraine . . . 16 Olena Pavliuk and Anastasiia-Olha Strontsitska

Power Consumption Analysis at MAC-Sublayer of Wireless Sensor

Networks . . . 27 Olha Bilyk and Kvitoslava Obelovska

Optimal Control with Prediction for the Process of Vacuum

Membrane Distillation . . . 37 Bogdan Korniyenko, Lesya Ladieva, and Oleg Bereza

Improved Quantum Genetic Algorithm on Multilevel Quantum

Systems for 0-1 Knapsack Problem . . . 51 Valerii Tkachuk and Mykola Kozlenko

Edge Intelligence for Medical Applications Under Field Conditions. . . . 71 Vlad Taran, Yuri Gordienko, Oleksandr Rokovyi, Oleg Alienin,

Yuriy Kochura, and Sergii Stirenko

Multipath Routing in Intelligent Transport Networks . . . 81 Yurii Kulakov, Alla Kohan, and Yuliia Hrabovenko

Artiﬁcial Intelligence Platform for Distant Computer-Aided Detection

(CADe) and Computer-Aided Diagnosis (CADx) of Human Diseases. . . 91 Oleg Alienin, Oleksandr Rokovyi, Yuri Gordienko, Yuriy Kochura,

Vlad Taran, and Sergii Stirenko

ix

Modiﬁcation of the LSB Implementation Method of Digital

Watermarks. . . 101 Bohdana Havrysh, Oleksandr Tymchenko, and Ivan Izonin

Datalogical Model of Dialogue Script. . . 112 Anatolii Verlan and Igor Chimir

Modiﬁed Method of Cryptocurrency Exchange Rate Forecasting

Based on ARIMA Class Models with Data Veriﬁcation. . . 123 Anastasiia Holiachenko, Lesya Lyushenko, and Oleksii Strutsynsky

Electrocardiogram Effective Analysis Based on the Random Forest

Model with Preselected Parameters . . . 137 Taras Panchenko, Andrii Yavorskyi, and Zhengbing Hu

Digital Technology: Emerging Issue for Agriculture . . . 146 Maryna Nehrey and Larysa Zomchak

Neural Network Method of Items Catalog Forming

for Online Store. . . 157 Ivan Kit, Hrystyna Lipyanina-Goncharenko, Taras Lendyuk,

Anatoliy Sachenko, and Myroslav Komar

Methods of Constructing a Lighting Control System for Wireless

Sensor Network“Smart Home”. . . 170 Andriy Dudnik, Serhii Dorozhynskyi, Sergii Grinenko,

Oleksandr Usachenko, Borys Vorovych, and Olexander Grinenko Material Planning with Hybrid Weed Invasion Algorithm Under

Cutting Problem Constraints . . . 180 Wenjie Xie

Advances in Technological and Educational Approaches

Teaching Reform of Supply Chain Management Based on the Concept

of Autonomous Learning . . . 193 Zaitao Wang and Ting Zhao

Digitalization of the Educational Process of Training Future

Engineering-Teachers. . . 204 Olesia Nechuiviter, Halyna Sazhko, and Anastasiia Kovalchuk

Application of POA in CET-4 Translation Teaching . . . 214 Jinling Xia and Huafeng Liu

Strategic Choice of University Logistics Management Major Based

on SWOT-AHP . . . 222 Chen Chen

Adoption of the OMNET++ Simulator for the Computer Networks

Learning: A Case Study in CSMA Schemes. . . 234 Kvitoslava Obelovska and Ivan Danych

Teaching Reform and Practice of the Trinity of Value, Knowledge

and Ability Under Blending Teaching . . . 244 Yanhong Ge, Kaixiong Hu, and Yanying Du

Building Multi-dimensional Professional Characteristics Under the Situation of University Transformation—Taking Automobile Service

Engineering as an Example . . . 256 Lu Ban, Yi Wei, and Daming Huang

Analysis on the Training Strategy of Applied Logistics Talents in the

New Era Under CDIO Mode. . . 265 Zhong Zheng, Liwei Li, and GengE Zhang

Research on the Ability and Quality Index of“Double-Position and

Dual-Ability”Teachers in the Applied Undergraduate Colleges. . . 279 Saipeng Xing, Weihui Du, and Qinxian Chen

Research on Blending Learning Innovation Model of International

Logistics Bilingual Course . . . 292 Xin Li, Yong Wang, Hong Jiang, Yawei Li, Sijie Dong, Ning Xiang,

Mengqiu Wang, and Saiwen Liu

Study on Online Teaching Experience Related to Ideological and Political Theory Courses in Higher Vocational Colleges Within the

Duration of Pandemic Prevention and Control . . . 301 Lili Li and Feifei Hu

Teaching Design and Curriculum Reconstruction Based on BOPPPS

Model in the Cultivation of Logistics Talents. . . 316 Geng E. Zhang, Jing Zuo, Fang Huang, and Liwei Li

Question Inquiry and Countermeasure Analysis of Educational

Evaluation Reform in Chinese Universities . . . 327 Ming Li, Chen Qi, Wei Wang, and Wanqiu Dong

“Integrated”Ideological and Political Education System for TCSOL

Major. . . 336 Haifeng Yang, Junhua Chen, and Xinyi Zhan

Research on Gold Course Construction of Railway Logistics

Management Under Double High School Background. . . 346 Qin Yang

Construction of Ability and Quality Model of Engineering Talents

Based on Analytic Hierarchy Process. . . 356 Jing Zuo, GengE Zhang, and Fang Huang

Intelligent Course Design of Automatic Warehouse Based on

Association Simulation. . . 367 Xiaoping Qiu, Cong Lan, Jun Liu, and Jiong Chen

Modeling in Logistics Engineering

Diagnosis of Atypical Forms of Myocardial Infarction Based

on Fuzzy Logic. . . 381 Nataliya Mutovkina and Alexey Borodulin

Coordination of Expert Assessments in the Diagnosis of the Technical

Condition of Medical Equipment. . . 392 Nataliya Mutovkina

Economic Relevance Between China’s Cross-Border Logistics

and E-commerce. . . 402 Xiyao Hou

Evaluation Index System of Core Competitiveness of Small and

Medium-Sized Logistics Enterprises in Nanning . . . 416 Zhong Zheng, Jingzuo Wang, and Liwei Li

Promising Modern Steerable Parachute for Unmanned Aircraft

Systems . . . 431 Volodymyr Alieksieiev, Pavlo Kazan, Olha Korolova,

and Ivanna Dronyuk

Enterprise Supplier Evaluation Model Based on Entropy Weight

Method in Calculus Learning. . . 440 Tao Chen and Lei Hu

Method of Extracting Formant Frequencies Based on

a Vocal Signal . . . 448 Serhii Zybin and Yana Bielozorova

Competitiveness of Comprehensive Freight Channel Based on Generalized Cost—Taking Container Transportation

as an Example . . . 458 Hongyu Wu, Jia Tian, Xiaoqing Zhang, and Chengzhi Liu

Devices on Inhomogeneous Links with Nonlinear Capacity . . . 469 Valerii Kozlovskyi, Andrey Bieliatynskyi, Vitaliy Klobukov,

and Vladyslav Dudnyk

Investigation of the Multicast Routing Model with Support of Trafﬁc

Engineering and Its Application in Software-Deﬁned Networking ^{. . . . .} 481
Zhengbing Hu, Oleksandr Lemeshko, Oleksandra Yeremenko,

Amal Mersni, and Maryna Yevdokymenko

Electricity Tariff Structures Modeling for Reengineering Ukrainian

Energy Sector. . . 493 Nataliia Klymenko and Maryna Nehrey

Optimization of Green Logistics Distribution Path-Taking JingDong

Distribution as an Example . . . 503 Xiaolin Zhang, Lijun Liang, and Mengwan Zhang

Raw Material Ordering Model Based on Data Processing

and Analysis. . . 515 Yi Huang and Tao Chen

Vehicle Routing Optimization of Urban Living Materials Distribution

Under Major Epidemic Situation. . . 525 Rongyan Zhu, Lei Li, and Fengjiao Wan

Design and Implementation of Non-avoidance Intelligent Parking

Device Based on Internet Plus Initiative. . . 538 Panyi and Wangmin

Research on the Development Strategy of China Railway Highspeed

Express in Guangxi Based on SWOT. . . 547 Jie Shang, Yang Li, Xuguang Wen, and Zhitian Ning

Optimization Model of Warehouse Picking Path Based on Simulated

Annealing Algorithm . . . 555 Bingchan Fan

Advances in Management and Application

Overview and Comparison of the Main Approaches to the

Implementation of Contact Tracing Mechanisms in the COVID-19

Pandemic . . . 567 Alexandr Kuznetsov, Yuriy Gorbenko, Anastasiia Kiian,

and Olha Bulhakova

Method of Obtaining Data from Open Scientiﬁc Sources and Social

Engineering Attack Simulation. . . 583 Roman Marusenko, Volodymyr Sokolov, and Ivan Bogachuk

College Teacher Training Management System and Work Strategy

Based on Competency Model. . . 595 Pingxin Tu and Fen Li

Development Countermeasures of Tianjin’s Modern Logistics

Industry Under the Background of Double Cycle Strategy . . . 605 Yuejuan Jing and Hongmei Gao

Carbon Emission of Commercial Logistics Under the Background

of Internet . . . 616 Yao Liu and Shengrong Lu

Information Technologies Implementation for Creative

Entrepreneurship and Innovations Development in Ukraine . . . 624 Iryna Moiseienko, Ivanna Dronyuk, Svitlana Vasylchak,

Mykola Kravchenko, and Uliana Petrynyak

The Inﬂuencing Mechanism of Job Stress, Job Satisfaction

and Job Burnout: A Case Study of Air Transportation. . . 634 Ping Liu, Yijun Wei, Yunjing Zhao, and Yi Zhang

Economic Growth and Capital Investment: The Empirical Evidence. . . 645 Larysa Zomchak and Maryna Nehrey

The Improvement of Electric Vehicle Charging Service Level Based

on Multi-objective Model. . . 653 Xiaohua Mo, Yan Chen, and Min Sun

Female Executives and Gender Pay Gap: Empirical Evidence

from A-share Listed Companies in Logistics Industry . . . 667 Jiangning Hu

Early Warning and Positioning of the Operating Risk of Chinese

Manufacturing Listed Companies Based on the Kalman Filter . . . 677 Zhihong Zeng, Youtang Zhang, Quanfang Xiao, and Xiaochen Sun

The Application of Artiﬁcial Intelligence in Organizational Innovation Management: Take the Autonomous Driving Technology of Tesla as

an Example . . . 690 Gubo Huang and Yan Yu

Research on the Development Trend of Teachers’Professional

Development Model in Open University. . . 698 Qin Ang, Xiaoqing Hong, and Yanan Ji

Management Status Analysis and Path Optimization of College

Student Societies from the Perspective of Student Satisfaction. . . 709 Xiangxing Yan, Yaqing Niu, Zilin He, Jiacheng Ma, Yimeng Wang,

and Dong Liu

Author Index. . . 725

**Mathematical Advances in Schemes**

**for Logistics Engineering**

**by the Structure of the Convolutional Neural** **Network Modifying**

Valentyn Kuzmych^{(}B^{)}and Mykhailo Novotarskyi

Department of Computer Engineering, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

**Abstract.** The main problem with simulating the partial differential equation
(PDE) solution process using neural networks is the need to increase the accuracy
and size of the domain. This paper proposes improving the convolutional neural
network (CNN) architecture to simulate solving a boundary value problem based
on the Poisson equation with arbitrary Dirichlet and Neumann boundary condi-
tions, which reduces the time of calculations by 3.36 times with an increase in
accuracy of calculations by 1.4 times. We achieve the obtained result by modify-
ing the CNN’s architecture at the stages of data input and their further processing.

The paper compares available approaches to modeling this problem’s solution and the solution’s results by the finite element method. We obtained the best results in both cases, showing relevant practical study examples.

**Keywords:**Machine learning·Poisson equation·Convolutional neural
network·CNN

**1 Introduction**

CFD (computational fluid dynamics) modeling is used to determine the distribution of pressure, velocity, and other movement parameters of liquids or gases. Finite Difference Method, Finite Volume Method, and Finite Element Method are based techniques for solving such various physical problems as weather forecasting and life sciences. Nev- ertheless, these methods have several limitations. The main one is a significant increase in computation time and memory usage with increasing domain size. We can reduce the solution time by applying the finite difference method to obtain a tridiagonal matrix.

This matrix structure allows parallel calculations, significantly reducing the total time to solve the problem. However, this approach is practical only when using domains with simple geometry because complex domains will significantly increase the risk of losing the convergence of the finite difference method.

These limitations prevent using numerical methods in real-time programs and encourage the active study of alternative methods for PDE solving.

The use of artificial neural networks (ANN) seems promising to solve these problems.

This opportunity is due to significant advances in deep machine learning. That is why

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ICAILE 2022, LNDECT 135, pp. 3–15, 2022.

https://doi.org/10.1007/978-3-031-04809-8_1

this approach is developing rapidly and includes the study of the effectiveness of using different types of ANN to solve boundary value problems.

Biomedical engineering is one of the areas of research where deep learning algo- rithms are popular. In most cases, this is because the accuracy of modeling biological objects plays a minor role compared to modeling speed. Moreover, GPU acceleration in the simulation of artificial neural networks can be a new practical solution to many biomedical problems.

This approach is essential in modeling pressure distribution in the human digestive tract due to reconstructive surgery. Determining the pressure field in the area of recon- structive surgery can be described by the Poisson equation. For operational decisions, modeling accuracy is not very important compared to obtaining simulation results in real time. That is why we consider using artificial neural networks as an alternative to numerical methods to solve this problem.

This paper aims to develop and train an artificial neural network to improve the parameters of the pressure field modeling in areas of the human digestive tract, which have complex geometry and boundary conditions.

**2 Literature Review**

We use CFD in many areas of research and industry. See, for example, such a study on Tu [1]. However, all numerical methods have several disadvantages, described by Wu & Ferng [2]. The most important of the disadvantages is the significant increase in computational time in large areas with complex geometry. The finite difference method can partially overcome this shortcoming by parallelizing its calculations, as shown in Simon, Gropp & Lusk [3]. However, to achieve convergence of this method, we must only use simple domain geometry or adaptive meshes. In particular, Rennels, Agrawal, and others [4] demonstrated this approach in their paper.

Recent decades have been successful in machine learning and developing deep neural networks. Raghu & Schmidt [5] presented a detailed survey of deep learning neural networks for scientific studies. Successes in developing new neural network structures have allowed us to take the next step in modeling physical processes. We can find the first publications on simulating the solution of PDE using machine learning in the early 90’s.

Dissanayake & Phan-Thien [6] developed a multilayer perceptron to solve nonlinear problems, such as the Poisson equation and thermal conduction with nonlinear heat generation.

Lee and Kang [7] proposed creating neural algorithms for solving differential equa- tions. Sirignano & Spiliopoulos [8] also used a similar approach in developing an algo- rithm for deep learning to solve partial differential equations. The main shortcomings of this period are a small set of boundary conditions (BC), a specific range of simulated functions of the right-hand side (RHS), and small domain sizes.

The beginning of the 2000s showed significant improvement in computational effi- ciency. As a result, many more studies were published, presenting more complicated and robust models. Smaoui & Al-Enezi proposed multilayer perceptrons for predicting orthogonal decomposition of the 2D Navier-Stokes equation and the 1D Kuramoto- Sivashinsky equation. Yadav and Kumar [10] conducted a more profound and complex overview of the methods and techniques.

Xiao et al. [11] and Tompson et al. [12] were the first to research the use of CNN to solve the Poisson equation. They proposed similar approaches to solve a boundary value problem based on the Poisson equation with a given RHS function. Nevertheless, to simulate the process of solving the Poisson equation in the real world, the structure of the CNN should be improved to reduce the time of PDE solving with the condition of preserving or even improving the accuracy.

**3 Problem Statement**

The Poisson equation is an elliptic partial differential equation. The solution of this
equation is presented as a boundary value problem in a rectangular domain with
parameters*(x,y)*∈[0*,n]*×[0*,m]. The following formulas can mathematically represent*
this problem:

⎧⎪

⎪⎪

⎪⎪

⎨

⎪⎪

⎪⎪

⎪⎩

*Δu(x,y)*=*F(x,y),*
*u(x,*0)=ϕ1*(x),*
*u(0,y)*=ϕ2*(y),*
*u(x,m)*=ϕ3*(x),*
*u(n,y)*=ϕ4*(y).*

(1)

We introduce a uniform grid to construct a difference scheme for the boundary value
problem (1):*ω**h*=

*x**i*=*ih,y**j*=*jh,i*=1*,n,j*=*jm*

, where*h*=1.

We discretize the boundary value problem (1) using the symbolic notation of dif-
ference operators. Next, we obtain the difference boundary value problem on the *ω**h*

grid:

⎧⎪

⎪⎪

⎪⎪

⎨

⎪⎪

⎪⎪

⎪⎩

−(*h**)u**i**,**j* =*f**i**,**j**,*
*u**i**,*0=ϕ1*(i)*
*u*0*,**j*=ϕ2*(j),*
*u**i**,**m*=ϕ3*(i),*
*u**n**,**j* =ϕ4*(j).*

(2)

We obtain an approximation of the Poisson equation for interior cells by using the second central difference to approximate the Laplace operator at an arbitrary interior cell with coordinates

*x**i**,y**j* and perform calculations on a five-point template:

−(*h**u)**i**,**j* =4u*i**,**j*−*u**i*−1*,**j*−*u**i*+1*,**j*−*u**i**,**j*−1−*u**i**,**j*+1

*h*^{2} =*f**i**,**j* (3)

Since we use a single sampling step, Eq. (3) has a simplified form:

*f**i**,**j*=4u*i**,**j*−*u**i*−1*,**j*−*u**i*+1*,**j*−*u**i**,**j*−1−*u**i**,**j*+1 (4)
There is no need to use the entire domainto get valuable results, only a particular
part. The object in the domainwith complex shape bounded by obstacles. The*(m*×*n)-*
matrix*dist*- represents the difference between regions:

*dist**ij*=

1*, (i,j)*−*node belongs to the obstacle region,*

0*, (i,j)*−*node belongs to the object region.* (5)

For all*(i,j)-cells withdist**ij* =1 we use*f**i**,**j* =0. Otherwise, function*f**i**,**j*is tabular.

The values of the*f**i**,**j*function can vary in the range [−1, 1]. Figure1shows example of
divided domain.

Calculations in Eq. (4) will be conducted only for those (i, j)-cells for which the following conditions are satisfied:

⎧⎪

⎪⎨

⎪⎪

⎩

*dist**i**,**j*+1=0*,*
*dist**i**,**j*−1=0,
*dist**i*+1*,**j* =0*,*
*dist**i*−1*,**j*=0.

*(1<i<n,*1*<j<m).*

The remaining cells belonging to the object may have 1, 2, or 3 neighbors located in the obstacle region. There may be various combinations of obstacle and object neighbor cells, and all of them can be obtained by rotating or mirroring the configurations shown in Fig.3.

**Fig. 1.** The yellow region is an obstacle, and a black region is an object

We use different approximation schemes for each of the following configurations:

– 4u*i**,**j*−*u**i*−1*,**j*−*u**i*+1*,**j*−2u*i**,**j*−1=*f**i**,**j*for the cell with one obstacle (Fig.3a),
– 4u*i**,**j*−*u**i**,**j*+1−*u**i**,**j*−1=*f**i**,**j*for two opposite obstacles (Fig.3b),

– 4u*i**,**j*−2u*i**,**j*−1−2u*i*+1*,**j*=*f**i**,**j*for two non-opposite obstacles (Fig.3c),
– 4u*i**,**j*−2u*i**,**j*+1=*f**i**,**j*for three obstacles (Fig.3d),

**Fig. 2.** The purple squares are obstacle cells, and the yellow squares are object cells

**i,j+1**

**i-1,j** **i,j** **i+1,j**

**i,j-1**
**i,j+1**

**i-1,j** **i,j** **i+1,j**

**i,j-1**
**i,j+1**

**i-1,j** **i,j** **i+1,j**

**i,j-1**

**i,j+1**

**i-1,j** **i,j** **i+1,j**

**i,j-1**

A B

C D

**Fig. 3.** Basic combinations of obstacle and object neighbor cells.

We assume that*f**i**,**j* =0 if*i*and*j*are outside the domain.

Transformation (2) into a linear algebraic equation system allows this boundary value problem to solve by calculating the unknown value for each cell (Fig.2).

**4 Methodology**

The neural network’s architecture is the critical component to achieving our objective, and this fact demands the methodology of designing NN architecture. In most of the considered articles, the authors use simple solutions, such as multilayer perceptrons or sophisticated architectures, which do not apply to the goal of our study. In recent

pre_conv residual_1 residual_2 residual_3

conv_2d

up_sampling_2d

conv_2d conv_2d conv_2d

up_sampling_2d

up_sampling_2d

output_conv

output (RHS) f_input

dist_input

Bottom-Up Pathway

Top-Down Pathway

CONCAT CONCAT CONCAT CONCAT

**Fig. 4.** The general structure of the ANN

papers on this topic, CNNs have proven the best. For these reasons, we have chosen a feed-forward CNN [18] as a baseline methodology for designing ANN architecture.

Firstly, we defined the format of input data for the model. The input samples are two tensors of size 96×96 - the first matrix is the RHS of the Poisson equation, and the second matrix encodes the geometric space - forms the input sample. The rule of calculating values of the elements of the second matrix is the following: if the grid cell belongs to the obstacle area, then the corresponding matrix element is zero. Otherwise, the value of the matrix element is equal to the distance to the nearest obstacle cell divided by 96√

2. An example of geometry and respective encoding we can see in Fig.5. We introduced this approach to encoding the geometric space and form input data because of the behavior of CNN – distance matrix preserves information about a high-level feature (distance to

obstacle) at the last convolutional layer (block “residual_3”). Furthermore, this method of forming input data helps achieve better accuracy of the neural network than the naïve approach – passing only RHS of the Poisson equation to the model without information about the spatial structure of the modeling area.

The second step is the composition of the inner structure of the architecture – the part between input and output. We used features from the Feature Pyramid Network (FPN) family of neural networks [13]. We kept the general structure of the FPN – neural network consists of two parts - “bottom-up pathway” and “top-down pathway.” We can see the general structure of ANN in Fig.4. The purpose of the bottom-up pathway is to extract features at different levels – from low-level features, which represent a particular cell and its neighborhood, to high-level features representing the whole modeling area. The top-down pathway combines all extracted features because it allows obtaining accurate solutions. To achieve our goals, we introduced significant modifications to the base methodology. We reduced the number of blocks in each pathway to four blocks. In addition, we decreased the number of trainable parameters in each convolutional layer.

Furthermore, we obtained 337447 trainable parameters – in contrast to the original network with 23534592 trainable parameters—these modifications allowed us to reduce the problem-solving time while maintaining sufficient accuracy.

Finally, we defined the output of the neural network. The output of most CNNs is 2–3 dense, fully connected layers. Despite the potential high accuracy for such an approach, this factor can slow down the computational speed of the model. To overcome this factor, the output block of our model consists of two convolution layers: first with seven filters and kernel with size 3, and last with one filter, kernel with size three and hyperbolic tangent activation function, which gives values in the range from -1 to 1.

We used the hyperbolic activation function because of specific features of the dataset, which we describe below. This approach to design the network’s output helps prevent increasing computational time.

The training dataset contains 40000 pairs of samples, where the feature is two matri- ces of size 96×96. One of the matrices is the RGS, and the other matrix specifies the

**Fig. 5.** The left figure is the geometry of the zone; yellow color represents the obstacle zone; the
light shades of the adjacent figure correspond to the values of the elements of the distance matrix
to the nearest obstacle

geometry of the space. The target matrix of size 96×96 represents the solution of the Poisson equation. We used Python algebraic multigrid PyAMG package to compute the solution [14].

The prepared set of different domains has 140 geometries, and we generated 250 RHS matrices and corresponding solutions for each geometry. Therefore, the complete training set included 35,000 samples.

Figure6demonstrates some examples of such a generated data set. To maintain the variability of the training dataset, we generated 5000 additional samples without any geometries. An example of such samples we present in Fig.7. In this case, all distance matrix values were equal to 1. RHS matrices were created by generating grids with lower resolution, with sizes 8×8, 12×12, and 16×16 with random values from−1 to 1, and then upscale generated grids to target size - 96×96, using cubic interpolation.

**Fig. 6.** Left column - RHS of the equation, right - respective solutions; white color denotes
obstacles

**Fig. 7.** Scenario without obstacles. Left column - RHS of equation, right - respective solution

Each sample pair contains an array with equation solution, i.e., target value. However, those values are significantly bigger than [−1, 1]. To provide stability of network training, we normalize all values of the generated solution with 0 for the mean value and 1 for the standard deviation value and rescaled to the range [−1, 1]. We used the scikit-learn library for data normalization and scaling [15]. Those values are the final target variable of the training process.

We used framework TensorFlow 2.4.1 to implement the model, with Adam weight optimizer [16], with following parameters: learning_rate=0.001, beta_1=0.9, beta_2

=0.999, epsilon=1e-7. We choose mean square error as a loss function during training.

The training was conducted on GPU MSI GeForce GTX 1660 Super Ventus OC 6 GB GDDR6, during 300 epochs and with a batch size of 32.

**5 Experiments**

We used the same hardware to train the model and for the experiment. We prepared 20 test geometries and generated 70 test samples for each geometry and 250 samples with geometries without obstacles as a test dataset to estimate the accuracy of the trained model. We used the MSE metric to determine the accuracy and achieved a 0.000516 value on the test dataset.

Our goal is to accelerate the simulation of the PDE solution to make our approach applicable in real-time. An important example of this case is the preparation for recon- structive surgery on the human digestive tract, so we chose a human stomach model.

The stomach model includes a normal state and a state of anastomosis (Fig.8).

We achieved an MSE accuracy simulation of the solution of the boundary value problem 0.000185 in the first case and 0.000344 in the second case. Results demonstrated in Fig.9and10. That results show the ability of the neural network to predict areas with high and low values, especially in the bottom part of the stomach.

We compared our model with numerical method and the most similar deep learning approach.

Gain of the modeling speed acceleration we measured compared to the numerical method. The PyAmg package we used to implement the numerical method. We measured the time of solving the boundary value problem on 1, 10, 50, 100, 200, 500, and 1000 samples, which simultaneously transferred to the trained model. Because of the ability of ANN to handle many samples simultaneously using GPU, the highest speed acceleration gain we achieved on 500 samples (Table1and Fig.11). After the number increase of samples, we observed a decrease in acceleration. It is possible to explain it by limiting the hardware we used for experiments.

We chose the approach proposed in Özbay AG et al. [17] as the most suitable method for comparison with our model. We also compared the computation time for a single sample for each approach. The article’s authors did not mention how they measured the computational time - from sample to sample or with batches of samples. Given this fact, we chose our worst case. The results of the comparison are in Table2.

**Fig. 8.** Left –normal stomach, right – anastomosis

**Table 1.** Comparison of NN and numerical method speed performance
Number of

samples

Total time – NN, ms

Time per sample – NN, ms

Total time – numerical method, ms

Time per sample – numerical method, ms

1 23,80 23,80 237,00 237,00

10 29,00 2,90 7460,00 746,00

50 55,80 1,12 31400,00 628,00

100 91,20 0,91 52600,00 526,00

200 159,00 0,80 99000,00 495,00

500 334,00 0,67 261000,00 522,00

1000 725,00 0,73 536000,00 536,00

Table2 shows that our approach has better accuracy and 3,36×(236%) gain in computational speed, even in the worst scenario. Moreover, our network additionally processes Neumann BC.

**Table 2.** Comparison of our NN and Poisson CNN

Model Time per – NN, ms MAE

Our model 23,80 0,0102

Poisson CNN 80,2 0,025

**Fig. 9.** Normal stomach; left - RHS of equation, center - network prediction, right - ground truth;

white color denotes obstacles

**Fig. 10.** Anastomosis; left - RHS of equation, center - network prediction, right - ground truth;

white color denotes obstacles

**Fig. 11.** Dependency of efficiency gain from a number of samples

**6 Discussion**

In order to ensure the effectiveness of the proposed approach, we conducted a simulation of the process of solving the boundary value problem based on the Poisson equation using the CNN described in this paper. We compared the obtained solution time with the solution time by the traditional numerical method and with the time of modeling the solution process on the structure of the CNN known from the literature. Both comparisons have shown that using the proposed CNN reduces the time of solving the mentioned boundary value problem.

However, during the study of solving the boundary value problem using different tensors of the RHS function, we found the shortcomings of the proposed approach to reducing computing resources. The main disadvantage is the reduced sensitivity of this network when processing data with small value gradients. We intend to address this shortcoming by pre-processing the data to increase the gradients without losing the consistency of the original data.

**7 Conclusions**

The main paper idea is modifying the CNN structure to reduce simulation time for solving boundary value problems while maintaining acceptable accuracy. We have improved the simulating process parameters on the example of solving the Poisson equation with Dirichlet and Neumann boundary conditions compared to known solutions, reducing the time to obtain simulating results in the fixed-size 96×96.

Experiments also showed a decrease in the time of solving the boundary value problem compared to the numerical method.

Acceptable loss in prediction accuracy and previously mentioned efficiency gain open opportunities to apply convolutional neural network-based techniques in various engineering and science fields, where modeling speed plays a crucial role.

In this paper, the proposed structure of the convolutional neural network demonstrates the process of modeling the boundary value problem based on the Poisson equation, which describes the distribution of pressure in the human stomach during reconstructive surgery. This analysis is related to the critical simulation time, maintaining acceptable accuracy.

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**for Covid-19 Analysis and Forecasting** **in Ukraine**

Olena Pavliuk^{(}B^{)}and Anastasiia-Olha Strontsitska

Lviv Polytechnic National University, S. Bandera str., 12, Lviv 79013, Ukraine [email protected]

**Abstract.** With the rapid spread of the Covid-19 pandemic in Ukraine, there is a
need to use existing and develop new methods for its analysis and forecast. This
article proposes a machine learning model that analyzes and provides a short-term
forecast of the pandemic in Ukraine based on “standard” open source statistics
and the six most commonly used Covid-related phrases in Google Trends. The
lost information was restored using power polynomials. Covid-19 distribution in
Ukraine was analyzed for each pandemic wave using correlation dependences
with Pearson’s correlation coefficients. It has been proven that the increase in the
number of laboratory-confirmed Covid cases in Ukraine is happening right before
the increase in Google user activity on this topic. 8 models based on SGTM neural
structures were developed to study the average weekly data, both reduced and not
reduced to the range from 0 to 1. In the most accurate model that implemented
a short-term forecast of laboratory-confirmed cases of Covid in Ukraine, the root
square error was 5.55%.

**Keywords:**Covid·Prediction·Coronavirus·Pandemic·SGTM neural-like
structures·Data mining·Google trends·Pandas

**1 Introduction**

For the first time in Ukraine SARS-CoV-2 was confirmed on February 21, 2020. Starting from August 1, 2020, according to the decision of the State Commission of Technogenic and Environmental Safety and Emergencies and indicators for determining the levels of epidemic danger, Ukraine was divided into quarantine zones [1,2]. Different colours were assigned to them: red - the most dangerous, orange - safer than red; yellow - almost safe; green - safe. The conditions for the transition of Ukraine’s regions to a new epidemi- ological zone are periodically reviewed and updated (approximately weekly). Residents are required to wear protective masks, adhere to social distance and other restrictions imposed in a particular quarantine area. As a result, supply chains were disrupted, which had a negative impact on local and international trade, leading to an economic crisis.

The business sector has been severely affected by quarantine restrictions, as there are restrictions not only in Ukraine but also around the world [3–6].

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 Z. Hu et al. (Eds.): ICAILE 2022, LNDECT 135, pp. 16–26, 2022.

https://doi.org/10.1007/978-3-031-04809-8_2

During the entire period of the Covid pandemic in Ukraine, three waves were iden- tified. The first lasted almost a year: from February 21, 2020 to mid-February 2021.

The second until mid-July 2021. Next is the 3rd wave, which continues to this day.

In early November 2021, Ukraine was ranked 2nd in coronavirus mortality in Europe.

Attempts to diagnose and predict the spread of the coronavirus pandemic were carried out using: mathematical models [7–9], artificial intelligence [10,11], machine learning [11,12], Bayesian networks [8,11], polynomial regression [8,11], etc. Therefore, an extremely important task is to develop an artificial intelligence system that summarizes previous research to forecast the spread of Covid in Ukraine. The combined machine learning model presented in this article is based on Data Mining and Machine learning technologies. With its help, we will analyze and forecast Covid-19 in Ukraine.

It is obvious that the interest of users of the global Internet grows with the spread of the pandemic. Given the stressful escalation of the situation about the coronavirus in the media and waiting for a laboratory-confirmed test result, users begin to search for information using search engines. Most of their actions occur in stressful conditions that take into account cognitive psychology [14,15]. By classifying queries related to COVID in Ukraine, one can get a knowledge base. Modern statistical data collection systems contain the following “standard” information about COVID: number of patients; number of deaths; those who have recovered; currently ill, etc. However, it is also important to classify COVID-related queries on Google’s search engine on the Internet. Google Trends data on the coronavirus pandemic have previously been used to study the spread of COVID [16–18]. However, it was not used to analysis and forecasting the spread of the pandemic in Ukraine. Google Trends offers a new approach to potentially predicting pandemic change by tracking people’s concerns about their searches.

Based on these data, it is possible to determine the correlations between queries in the Google search engine related to the coronavirus pandemic, and the future surge in the number of patients and deaths from COVID in Ukraine. Since they have lost data, they are restored if necessary by polynomials of 5th and 6th degrees. Noise in the data is eliminated by smoothing with a simple moving average. Because the data have different values, which can vary by an order of magnitude or more, it is advisable to bring them to the range from 0 to 1. Applying correlation analysis to “standard” and obtained from Google search server statistics, you can create a knowledge base. Only include Covid- related data that is relevant to Ukraine. On the basis of the created knowledge base with the help of such means of artificial intelligence as neural networks it is possible to carry out high-precision short-term forecast on-line. Neural-Like Structures Based on Geometric Data Transformations (SGTM neural-like structure) were used for the forecast [19,20]. The results of the forecast are visualized in the form of tables and graphs, which, if necessary, can be saved in the archive of forecasts for comparison and analysis.

**2 Materials and Methods**

**2.1 Filling Out the Knowledge Base**

“Standard” statistics about “Covid” are obtained from open sources of the sitehttps://

ourworldindata.org/coronavirus/country/ukraine. As the data file is large (21.3 MB) and

contains information about Covid around the world, only those data that relate to Ukraine have been filtered. This file has a size of 180 KB.

After analyzing the obtained data, it was found that their partial loss, i.e., for some parameters records in the database were missing, or in their place were recorded zeros.

Therefore, there is a need to supplement and smooth them. The simplest and at the same time the most effective method of addition is the use of power polynomials, which was used in this work. The choice of the degree of a polynomial depends on the specific parameter that describes Covid in Ukraine and its values. For example, in Fig.1a and b. the blue color shows an example of lost data on such a parameter as “new tests” for 2020 and 2021, respectively. The trend in the form of a power polynomial is reflected in black.

**Fig. 1.** An example of determining the trend using a power polynomial to supplement the lost
data on the parameter “new tests”.

The criterion for choosing the degree of the polynomial is the maximum value of the
approximation value R^{2}. In both cases, the best result was shown by the polynomial of the
6th degree. For the parameter “new tests” in 2020, R^{2}=0.727, which indicates its rather
good approximation properties. In 2021, the value of the reliability of the approximation
was R^{2}=0.529, i.e., the polynomial showed a worse approximation compared to 2020.

However, the amount of lost data was greater, and the form of the graph was much more complex. The obtained values of the polynomial are supplemented by the lost data.

Similarly, lost data for all parameters in Covid statistics in Ukraine were recovered. It has been experimentally established that the trends of these parameters most accurately describe polynomials of the 5th and 6th degrees. Since the developed SSI must work in the ‘on-line’ mode, the use of higher degree polynomials is inexpedient, due to the complexity of the calculations, and the time spent on their implementation.

All Covid parameters in Ukraine have a significant stochastic component, so it is necessary to smooth them out. A simple moving average (SMA) was used for this purpose. The data is smoothed out at 7 points, because the data has a seasonal cyclic component, which is equal to 7 days, i.e., one week. Thus, the processed data is written to the knowledge base in the form of a file of almost 200 KB.

Another source of information is the queries of users in the Google search engine using the phrase “Covid” and its combinations in search phrases in Ukraine. The set of statistics was generated using Data Mining tools, namely Google Trends. The down- loaded data is written to a file containing 17 columns with detailed characteristics:

death, death Increase, in Icu Cumulative, in Icu Currently, death Increase, hospitalized Increase, hospitalized Currently, hospitalized Cumulative, negative, negative Increase, on Ventilator Cumulative, In Ventilator, on Ventilator. Because the amount of informa- tion downloaded was significant (190 Mb), there was a need to filter the most common phrases. For this purpose the software library for Pyton - Pandas is applied. It is a handy tool for reading and processing data. The following is a software solution for using Pandas to process daily COVID data (Fig.2).

**Fig. 2.** Software solution for using Pandas to process daily COVID data

Another thing to worry about is that Google data from user searches on the Internet is submitted weekly, and Covid data - daily. So it was decided to average the Covid data so that aggregate cases for each week were received, not daily data. This was done in two steps: first, 7 days were subtracted from the date so that it represented the first day of the week in question. Therefore, for example, the date 2021-03-01 denotes the week beginning on the first of March. Then a re-sample was made and averaged for each 7-day period (Fig.3).

**Fig. 3.** Software solution for using Pandas on a seven-day averaging of Covid data

For the purposes of this work, only seven columns from the data set were used:

“Week covid: (Ukraine)”; «Covid: (Ukraine)»; «Covid symptoms: (Ukraine)»; «Covid testing: (Ukraine)»; «Covid treatment: (Ukraine)»; “Coronavirus: (Ukraine)”; «Con- firmed cases: (Ukraine)». The obtained data are averaged over the week. The lost data is supplemented and smoothed in the same way as described above. The file size was 11 Kb and was also entered into the knowledge base.

**2.2 Preparation of Training and Test Data for SGTM Neural-Like Structures**
Although the size of the received files in the knowledge base is insignificant, they contain
parameters that do not correlate much with the confirmed cases of Covid in Ukraine.

Therefore, for the analysis of pandemic data, and the formation of training and test samples of SGTM neural-like structures, it is advisable to filter the data that correlate with each other. This is done using a matrix of correlation dependences constructed from the Pearson correlation coefficient. The dimension of the matrix was 6×6. The columns and rows of the matrix are: covid; covid symptoms; covid testing; covid treatment;

coronavirus; confirmed cases. The first 5 parameters were obtained from the knowledge base from the query data file in the Google system, and the last from the file with

“standard” statistics. Figure4shows the results obtained on the matrices of correlations.

**Fig. 4.** Matrices of correlations between Covid parameters in Ukraine (a, b, c, d - first, second,
third, and all pandemic waves, respectively)

On the main diagonal of the matrix is the maximum value of the Pearson corre- lation coefficient. This is obvious because the coefficient has a direct correlation with itself. Therefore, we will not take such data into account. The values in which the Pearson correlation coefficient is significant are highlighted in yellow in the matrices of correlation dependences. These are the following pairs of parameters for the entire pandemic period: coronavirus - confirmed cases; covid - coronavirus; with values of indi- cators 0,668902807; 0.421016699 respectively. The rest of the dependencies between the parameters are not so pronounced. In the general trend of the Covid-19 pandemic in Ukraine, the phrases “coronavirus” and “Covid” correlate with the number of clin- ically confirmed cases the most. Moreover, positive values of the Pearson correlation coefficient indicate a direct dependence (with the growth of one parameter - increases the other). In the first wave of the pandemic, the following pairs of parameters had the greatest correlation: coronavirus - confirmed cases; coronavirus - covid; covid symp- toms - covid testing; confirmed cases - covid. The emphasis on the entire pandemic has changed. Covid-19 was a new viral disease that most Internet users were still unaware of.

Therefore, they were more interested in the symptoms of this disease; how many people got it (clinically confirmed cases); where you can test for its presence; how to cure it. All parameters had a direct proportional relationship, except for one pair of confirmed cases - covid. No obvious dependence was observed, except for the pair coronavirus - con- firmed cases for which Pearson’s correlation coefficient was 0.537588797, which means that users trusted only clinically confirmed cases of coronavirus, all other parameters were of much less interest.

During the second wave of the pandemic, the following pairs of parameters corre- late mostly: coronavirus - confirmed cases; coronavirus - covid; confirmed cases-covid symptoms; coronavirus - covid symptoms. In contrast to the first wave of the pandemic, the second increased the number of parameters that correlate with clinically confirmed cases of the disease and it became much more well-known and searchable value among people. Moreover, the direct correlation dependence became almost twice as large for the first two parameters. And this shows that the same issues that previously interested in the future became even more interesting to users. Directly proportional dependence has become even 40% more popular. Also, almost twice less directly proportional depen- dence (Pearson’s correlation coefficient varied in the range from 0.41 to 0.43) have pairs:

confirmed cases - covid symptoms and coronavirus - covid symptoms. This suggests that interest in corona virus symptoms has increased relative to the first wave of the pandemic as new strains begin to appear.

The third wave of the pandemic is still going on. Therefore, Pearson’s correlation coefficients can be listed in the “on-line” mode. As of the beginning of November there is the following dependence between pairs of parameters: coronavirus - confirmed cases;

confirmed cases - covid; covid - coronavirus. Therefore, the training and test set of values will be formed by correlating parameters.

All types of data have a different range. For their further use in the process of learning SGTM neural-like structures, there was a need for scaling. It consisted in bringing the range from 0 to 1 by linear normalization.

**2.3 Machine Learning SGTM Neural-Like Structures**

SGTM neural-like structures (Fig.5) were used to predict the average number of con- firmed Covid cases in Ukraine. Its main advantage is the non-iterative learning process.

SGTM neural-like structures can be used to process large amounts of data. The time spent on training is determined in advance by a known number of conversion steps and depends only on the hardware. The whole data set was divided into training and test sets.

**Fig. 5.** SGTM neural-like structures

To implement the Covid pandemic forecast in Ukraine, 8 models based on SGTM neural-like structures have been developed. Their inputs were fed a vector of input signals for parameters that correlated in each of the pandemic waves, and all generally given

in the range from 0 to 1. The outputs of the first 4 models - not scaled values of the number of laboratory-confirmed Covid cases in Ukraine. Scalable values were applied to the other 4 models. SGTM neural-like structures were trained in supervised training.

**3 Modeling and Results**

All the above steps are presented in the form of elements of an artificial intelligence system (AIS). It analyzes statistics on coronavirus in Ukraine, as well as implements a short-term forecast. Schematically, SSI for short-term prognosis of clinically confirmed Covid cases in Ukraine is shown in Fig.6.

**Fig. 6.** Block diagram of the artificial intelligence system according to the forecast of Covid’s
spread in Ukraine

Training and test samples of SGTM neural-like structures were formed according to the dominant parameters for each wave of coronavirus. Each SGTM neural-like struc- tures will predict the parameters that correlate in each individual wave of the pandemic.

Also, a separate ANN is trained for parameters that correlate in all waves of the pan- demic together. Each model is designed for normalized and non-normalized output signals. These 8 ANN variants with different number of input parameters were used for the controlled learning mode of SGTM neural-like structures. Given the importance of short-term forecast, all but the last implementation were included in the training set, and the latter - in the test.

**4 Comparison and Discussion**

Learning outcomes and predictions were evaluated by the standard error of the range.

The accuracy of the forecast was also checked by the absolute value of the deviation of the predicted data from the real laboratory-confirmed cases of Covid in Ukraine. The results of training and forecasting SGTM neural-like structures are presented in Table1.

**Table 1.** Results
List of input

parameters

Normalization of input data

Normalization of output data

SQRT training (%)

SQRT prediction (%)

ABS 1-coronavirus

2-covid 3-covid testing 4-covid symptoms 5-covid treatment 6-confirmed cases

+ − 5,65 5,55 734,0766

+ + 7,30 7,53 156,0378

1-coronavirus 2-covid 3-covid symptoms 4-confirmed cases

+ − 5,71 7,89 1211,446

+ + 7,31 7,53 188,6897

1-coronavirus 2-covid 3-confirmed cases

+ - 5,63 7,90 1281,127

+ + 7,31 7,53 191,7536

1-coronavirus 2-confirmed cases

+ - 5,69 7,95 991,811

+ + 7,30 7,53 157,7756

Predicted and normalized values obtained from 4 models of SGTM neural-like struc- tures of clinically confirmed cases of coronavirus in Ukraine were translated back accord- ing to linear normalization. The result was a range of values in the old bit grid. For convenience, the results are presented in the form of graphs (Fig.7). They can also be saved to a file if desired.

The results of all 8 models were highly accurate, the RMS error reduced to the range of values did not exceed 7.95%. And their results are comparable. Moreover, the accuracy of the predicted data using SGTM neural-like structures model with the maximum number of parameters and normalization of only the input data is higher and

its error does not exceed 5.55%. The calculated absolute values of deviations of the predicted values from the clinically confirmed values indicate that they do not exceed the defined errors.

**Fig. 7.** Predicted and actual values of clinically confirmed Covid cases in Ukraine.

**5 Conclusion**

The problem of predicting the Covid pandemic is one of the most important in the world in general, and in Ukraine in particular. Despite the significant amount of statistics collected in open sources, there is a need to restore and supplement them. The authors created a knowledge base, filling it with “standard” statistics, while identifying lost data and restoring them by power polynomials. For a more complete knowledge base, they used data that reflects the activity of users in the Google search engine. Using Data Mining tools such as Google Trends and Pandas, they filtered data on the most commonly used phrases related to coronavirus in Ukraine.

According to the calculated matrices of correlation dependences of the Pearson correlation coefficient, the parameters that are most significant for each wave of the pandemic were identified. They were used to analyze the social behavior of Google users. The relationship between the increase in the number of searches and the num- ber of laboratory-confirmed Covid cases in Ukraine was established. According to this dependence, it is possible to predict the future trend of coronavirus spread.

By normalizing the statistics to the range from 0 to 1, we created a training and test sample for SGTM neural-like structures. Based on it, 8 models were developed. In the model that gave the highest accuracy, the RMS error reduced to the range of values did not exceed 5.55%. This accuracy is high, given that the predicted data of the third wave of the coronavirus pandemic in Ukraine are close to the plateau. The deterioration of accuracy was also affected by the weekend, because on such days the number of laboratory-confirmed tests is much smaller.

To improve the accuracy of solving the problem of predicting confirmed cases of Covid, it is advisable to conduct further research in two main areas:

1) the use of other types of filters to recover lost data;

2) the use of non-iterative ANN with the possibility of multiple linear regression using a linear polynomial as a constructive formula for the structure of SGTM.

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