Department of Numerical Methods and Computer Modeling

The scientific activity of the staff of department No. 150 is aimed at advancing cutting-edge science in the following areas:

development and use of artificial intelligence tools in scientific research;
high-performance computing (HPC);
error theory, reliability of obtained computer results;
methods and algorithms for parallel and distributed computing for computers with different parallel architectures;
mathematical modeling of physico-mechanical processes with approximate input data on modern computers;
intelligent computer systems.

Artificial intelligence is actively developing in various fields of human activity. In department No. 150, for the first time in the world, tools for automatic image segmentation based on artificial intelligence and deep learning have been developed, which can be applied for machine learning in solving a wide range of computer vision tasks, including intelligent image and video processing. The results obtained in this direction can be implemented in algorithmic and software tools for modeling processes in various fields of human activity, particularly in medical and military areas. For the first time in the world, methods for recognizing the structure of sparse matrices of ultra-large volumes based on artificial intelligence and deep learning have been developed, enabling the automation of the computer selection process of the most efficient algorithm for solving computational mathematics problems on parallel computers of different architectures, using the "profile" of the sparse matrix. Using parallel computing with this approach, it was possible to reduce the time to solve complex problems in civil and industrial construction, nuclear energy, pipeline transport, strength analysis of structures, etc., by one to two orders of magnitude.

High-performance computing is an extremely important area of scientific research. The architecture of modern supercomputers is constantly becoming more complex. However, there are difficulties in their effective use: achieving maximum performance of parallel computations, scalability of application software, and adaptation to new architectural features of computers. As global experience in solving practical problems shows, there are already significant differences due to communication losses between the maximum and operational performance of computers. The emergence of ultra-powerful computers of various architectures (in the future – exaflop supercomputers) requires a new programming paradigm and the development of algorithmic and software tools.

Research has been conducted on the error theory of computer results in solving applied problems, and based on it, a technology for automatic computer investigation of the mathematical properties of computational mathematics problems with approximate data has been developed, using the required (arbitrary) precision, as well as analysis of the reliability of the obtained computer results.

In department No. 150, innovative adaptive methods and algorithmic software for solving computational and applied mathematics problems on parallel computers have been developed. The innovation of the approach lies in recognizing the mathematical properties of computer problems for pathological cases (degenerate and ill-conditioned systems of linear algebraic equations, multiple and close eigenvalues of matrices, etc.) using multi-precision arithmetic; automatic tuning to an efficient computing environment (various parallel architectures: MIMD, hybrid, multicore; different levels of RAM; features of connections between computing elements); automatic parallelization of computations, ensuring efficient use of computer resources.

A significant part of applied processes, as a result of mathematical modeling, boils down to solving computational mathematics problems with sparse data structures of ultra-large volumes. The reliability and efficiency of solving these problems on a computer largely determine the effectiveness of mathematical modeling. Solving the problems of creating or using existing algorithmic and software tools for reliable mathematical modeling of various processes on parallel computers of different architectures requires users – specialists from various fields – to have appropriate knowledge in computational mathematics, architectural features of computers, skills in using various parallel programming technologies, etc.

In department No. 150, an intelligent computer mathematics system InparSolver has been developed, which provides automatic execution of all stages of computer investigation of problem tasks: determining the structure of large-volume sparse data using artificial intelligence methods and reducing them to a regular form; investigating the mathematical properties of problems with approximate data and solving them with adaptive algorithms automatically tuned to an efficient computing environment, with reliability assessments of the results. The application of the intelligent system InparSolver and the intelligent interface based on it for mathematical modeling IIMM allows for a significant redistribution of tasks between the user and the computer compared to traditional technologies, reducing the development time of applied applications for solving scientific and technical problems and improving the quality of the obtained solutions.

LIST OF RESEARCH WORKS CARRIED OUT IN 2020-2024

R&D: project R 1.1.2 "Development of computer algorithms and a new generation of high-performance software tools for modeling and forecasting the condition and resource of critical welded structures"

Carried out within the framework of the targeted scientific research program of the NAS of Ukraine “Reliability and durability of materials, structures, equipment, and facilities (Resource-2)”, R&D codes: Stage 1 V.K.150.19.16, Stage 2 V.K.150.21.17, Stage 3 V.K.150.25.18, Stage 4 V.K.150.28.19, Stage 5 V.K.150.29.20, Q1 2016 – Q4 2020.

Results of R&D

New computer algorithms were developed for numerical forecasting of the condition of welded pipelines and pressure vessels considering nonlinear pre-critical failures, for statistical analysis of residual strength of welded pipelines and pressure vessels with detected local wall thinning defects using the Monte Carlo method.
A new generation of high-performance software tools for modeling and forecasting the condition and resource of critical welded structures based on parallel computing was developed.
Software with parallel computation organization was developed and integrated into the Weld-Predictions software suite (developed by the E.O. Paton Electric Welding Institute of the NAS of Ukraine) for solving computational problems of forecasting the load-bearing capacity of welded pipelines and pressure vessels with defects on hybrid architecture computers.
Computer solutions were obtained for a number of forecasting problems of load-bearing capacity of welded pipelines and pressure vessels with local metal loss defects considering nonlinear pre-critical failures for the E.O. Paton Electric Welding Institute of the NAS of Ukraine (significant reduction in mathematical modeling time was achieved).
The new generation of software tools for forecasting residual resource and operability of critical welded structures with detected operational defects was implemented at the E.O. Paton Electric Welding Institute of the NAS of Ukraine.

The R&D completion report was approved at the meeting of the Academic Council of the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine (Protocol dated 24.11.2020 on acceptance and evaluation of scientific work) and at the reporting session for Section 1 of the “RESOURCE-2” program on 22.12.2020.

R&D: "Develop new methods of parallel and distributed processing of very large data volumes for analysis of complex multicomponent environments"

Code V.F.K.150.20, Q1 2017 – Q4 2021.

Results of R&D

Structures of input data and properties of computational mathematics problems arising in practical tasks of analyzing complex multicomponent environments on parallel computers of various architectures were studied.
New efficient algorithms for parallel and distributed computations were developed for solving computational mathematics problems with very large data volumes arising in practical tasks of analyzing complex multicomponent environments on computers of various architectures based on automatic identification of input structure, structural regularization and decomposition of sparse data, and automatic verification of computational solution reliability.
New parallel fine-tile algorithms for solving linear algebra problems were developed, ensuring efficient use of resources of parallel computers of various architectures.
Network algorithms for processing very large data volumes for analysis of complex multicomponent environments were created.
The developed algorithmic and software tools are used for constructing optimal aerodynamic surface profiles (DP "Ilchenko-Progress") and for solving computational problems arising in modeling processes in the field of electric welding (E.O. Paton Electric Welding Institute of the NAS of Ukraine). There are no analogs of the developed algorithmic and software tools based on the developed methodology in the field of electric welding.

The R&D completion report was approved at the meeting of the Academic Council of the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine (Protocol No. 20 dated 07.12.2021 on acceptance and evaluation of scientific work).

R&D: "Develop an intelligent computer mathematics system for solving computational problems of mathematical modeling in science and engineering on hybrid architecture computers"

Code V.P.150.22, Q1 2018 – Q4 2020.

Results of R&D

Principles and methodology for computer research of mathematical models with approximate data were developed, implementing automatic adaptive tuning of the method, algorithm, and parallel computer topology according to problem properties.
An intelligent computer mathematics system (ICMS) was developed for automatic research and solving computational mathematics problems on computers with multicore and graphical processors based on the use of artificial intelligence elements and multi-precision arithmetic to ensure solution reliability.
InparSolver (an experimental ICMS prototype) was created and implemented as standard software for the SKIT supercomputer complex.

InparSolver is used in NAS Institutes of Ukraine (E.O. Paton Electric Welding Institute, S.P. Timoshenko Institute of Mechanics). Using InparSolver significantly increases user productivity and reduces time and resources for conducting physical experiments. There are no analogs of the ICMS InparSolver worldwide.

The R&D completion report was approved at the meeting of the Academic Council of the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine (Protocol No. 4 dated 24.11.2020 on acceptance and evaluation of scientific work).

R&D performed under contract: "Develop methods of high-performance computing for studying mathematical models of heterogeneous media and processing big data based on supercomputer technologies"

Code 7/2/267-10df / V.F.150.2.1230, Q1 2020 – Q4 2021.

Results of R&D

New adaptive computer methods and high-performance computing algorithms were developed for solving computational problems arising in mathematical modeling of the state of heterogeneous media and processes occurring within them.
New discrete mathematical models of the state of heterogeneous media and processes occurring within them were created, including fractional differential models for studying features of migration dynamics of soluble substances during groundwater filtration.
A promising architecture of specialized segments of a computing cluster for training and applying artificial neural networks was developed.

The proposed methods and computer algorithms were experimentally studied by solving a number of test and practical problems. The created methods and algorithms are used in NAS Institutes of Ukraine (E.O. Paton Electric Welding Institute, S.P. Timoshenko Institute of Mechanics) for mathematical modeling of the state of heterogeneous media and processes occurring within them.

The R&D completion report was approved at the meeting of the Academic Council of the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine (Protocol No. 20 dated 07.12.2021 on acceptance and evaluation of scientific work).

R&D: "Develop models and methods of heterogeneous computing for continuum mechanics problems"

Code V.F.150.26, Q1 2019 – Q4 2023.

Results of R&D

New models and methods of heterogeneous computing were developed, using a combination of MIMD and SIMD architectures, simultaneous use of different types and levels of memory, arbitrary precision, block processing of sparse data, multithreading, and software modules created by processor and graphics accelerator manufacturers.
New methods and algorithms for studying and solving basic computational mathematics problems with approximate data on heterogeneous computer systems with variable hardware and software were developed.
Methods of structural regularization of matrices for computational problems were developed; architecture and training of a convolutional neural network for automatic computer identification of structures and characteristics of sparse matrices were conducted.
Theoretical foundations and new block algorithms for high-performance computing using multi-precision and mixed-precision arithmetic for studying and solving linear algebra problems and systems of nonlinear equations on heterogeneous computers were developed.
A methodology for high-performance computing for studying and calculating mathematical models described by problems with a unique solution in a subspace, using the normal pseudoinverse solution of SLAE of discrete finite element models, was developed and substantiated.
New methods and computer algorithms of high-performance computing for studying and solving computational problems of continuum mechanics in a variable hardware and software environment of heterogeneous computers were developed: strength and stability analysis of structures, including composite materials, modeling and forecasting the condition and resource of critical welded structures, modeling heat transfer processes.

The developed methods and algorithms are applied to solve practical problems of continuum mechanics on modern high-performance computers for restoration and reconstruction of damaged or destroyed objects of military and civil infrastructure, primarily critical infrastructure, in defense, mechanical engineering, construction, and natural resource sectors. The developed algorithmic and software tools are used in NAS Institutes of Ukraine: V.M. Glushkov Institute of Cybernetics, E.O. Paton Electric Welding Institute, S.P. Timoshenko Institute of Mechanics.

The R&D completion report was approved at the meeting of the Academic Council of the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine (Protocol No. 18 dated 28.11.2023 on acceptance and evaluation of scientific work).

R&D "Develop adaptive algorithms of high-performance computing for mathematical modeling of physico-technical processes in a variable computer environment"

Code No. 8.22 MM / VKM 150.35.22, Q1 2021 – Q4 2023.

Results of R&D.

Algorithmic and software tools were developed for researching and solving linear algebra problems with sparse data structures, which enable automatic selection of the most efficient variable computer environment for solving a specific problem, as well as transforming matrices into one of the canonical forms (banded, skyscraper, profile, block-diagonal with framing) and applying efficient decomposition methods. The use of the created algorithmic and software tools significantly increases computational performance in mathematical modeling with very large systems of linear equations and algebraic eigenvalue problems (up to tens of millions) and provides numerical results with higher reliability. Used for mathematical modeling of stress-strain state, natural frequencies, and stability of building structures and their elements.

R&D "Develop an intelligent interface for modeling physico-mechanical processes based on parallel computing"

Code V.P.150.30, Q1 2022 – Q4 2024.

Results of R&D

An intelligent interface for automatic mathematical modeling (IIMM) of physico-mechanical processes with approximate data of very large volumes was developed and tested on the SKIT cluster complex, performing mathematical modeling of physico-mechanical processes: condition of critical welded structures; strength of building structures; stability of new composite materials, etc.

For testing IIMM, lifecycle computational models of welded structures, strength of building structures and facilities, and stability of composite materials were constructed. Using IIMM, on a hybrid computer, automatic research of a computational model with a priori uncertain properties is performed, and an efficient solution algorithm is built in a variable computer environment—the most effective for the specific computational model. Upon completion of computations, the obtained solution is provided with reliability estimates and explanations of the research process. For such research, IIMM uses knowledge-oriented technologies based on artificial intelligence methods, machine methods for research and solving problems with approximate data, employing multi-precision and mixed computation models on parallel, distributed, and hybrid architecture computers. As a result of using IIMM, users gain new knowledge about the mathematical properties of the computational model. By comparing obtained results with existing knowledge about the physico-mechanical object, applied users can identify shortcomings of the initial problem formulation, constructed mathematical model, etc., and warn against unforeseen catastrophes.

R&D performed under contract: "Develop a high-performance computing platform based on the SKIT supercomputer for cybersecurity, mathematical modeling, and engineering tasks"

Code V.P.150.4.1230, Q1 2023 – Q4 2024.

Results of R&D

In the Act dated December 31, 2024, of acceptance of the scientific project "Develop a high-performance computing platform based on the SKIT supercomputer for cybersecurity, mathematical modeling, and engineering tasks" for Stage II "Create a high-performance computing platform for solving mathematical modeling, discrete optimization, crypto- and steganalysis problems, and vulnerability detection based on SKIT supercomputers and conduct testing on test and practical tasks," performed according to the NAS of Ukraine Presidium resolution dated 13.12.2023 No. 443 "On budget financing of NAS of Ukraine in 2024" and Contract dated 01.01.2024 No. 2.1/24-P. Execution period: start January 1, 2024; end December 31, 2024, the following was noted:

A new generation of parallel and distributed computing algorithms was developed for mathematical modeling of objects, processes, and phenomena of various nature, discrete optimization, cryptanalysis, and vulnerability detection in software and hardware.
New block methods and adaptive computer algorithms of high-performance computing were developed for solving computational problems based on multi-precision and mixed-precision arithmetic arising in modeling objects, processes, and phenomena of various nature.
A two-dimensional fractional differential spatial non-isothermal moisture transfer model based on a linearized finite-difference scheme was constructed, and a multithreaded algorithm with dynamic time step adjustment was developed for solving initial-boundary value problems based on analysis of the required number of iterations for solving SLAE and its speed estimates.
Methods for organizing parallel work of portfolios of optimization algorithms based on modern multiprocessor computing complexes and advanced software technologies were developed.
A systematic approach to stability analysis and regularization of vector optimization problems under uncertainty and possible disturbances of input data using Pareto optimization was developed.
Methods and algorithms of high-performance computing for parallel and quantum computation models based on multi-precision arithmetic were developed for solving cryptanalysis problems in cybersecurity.
Behavior algebra templates were created and an algebraic matching algorithm for Intel x86 binary assembler code was implemented based on an insertion modeling system.

The report on the completion of Stage II of the scientific project was approved at the meeting of the Academic Council of the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine (protocol dated 26.11.2024 No. 18).

INTERNATIONAL SCIENTIFIC PROJECT

One of the important activities of the department is international cooperation. A team of young researchers from the department conducts scientific research under the International EIRENE Max Planck — Ukraine Cooperation & Mobility Grant program from the Max Planck Society (Germany). The research concerns sparse data structures in the context of high-performance computing (HPC) for solving linear algebra problems — adaptive algorithms and technologies. https://www.old.nas.gov.ua/UA/Messages/Pages/View.aspx?MessageID=10515, https://ukrainet.eu/2022/05/06/mps-ukraine/

In the Information-Analytical Bulletin No. 8, 2023 "Ways of Development of Ukrainian Science" (Supplement to the journal "Ukraine: Events, Facts, Comments") in the section "International Partnership for Ensuring the Sustainability of Science and Education in Ukraine," page 26, information is provided: "The team of young researchers of the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine was nominated for a grant under the EIRENE Max Planck-Ukraine Cooperation & Mobility Grant program from the Max Planck Society (Germany)," https://ukrainet.eu/2022/05/06/mps-ukraine/ https://nbuviap.gov.ua/images/informaciyni_vidanya/shliahi_rozv_nauki/2023/nauka08.2023.pdf

PROMOTION OF WIDE USE OF RESULTS BY THE SCIENTIFIC AND EDUCATIONAL COMMUNITY

Presentations at the 4th International Workshop of IT-professionals on Artificial Intelligence.

Articles in publications indexed in international scientometric databases Scopus and Web of Science.

Teaching at higher education institutions

Academician, Doctor of Physical and Mathematical Sciences, Professor O.M. Khimich taught special courses at NTUU "Igor Sikorsky Kyiv Polytechnic Institute" in 2018–2021: "Methods of Parallel and Distributed Computing," "Grid Systems and Cloud Computing Technologies"; https://intellect.kpi.ua/profile/xom2; since 2018, he has been teaching at Taras Shevchenko National University special courses: "Methods of Computer Research of Mathematical Models," "Methods of Parallel and Distributed Computing." https://incyb.kiev.ua/employee/khimich-oleksandr-mykolayovych, https://csc.knu.ua/uk/person/khimich

Senior researcher, Candidate of Physical and Mathematical Sciences teaches a special course "High-Performance Distributed Computing Systems" at Kamianets-Podilskyi University https://cs.kpnu.edu.ua/2024/09/19/sydoruk-volodymyr-anatolijoch/

RECOGNITION OF SCIENTIFIC ACHIEVEMENTS

Acts on the use of scientific developments have been obtained:

For the scientific work "Modeling of physico-technical processes based on parallel computing," V.A. Sydoruk and O.V. Chistyakov were awarded the President of Ukraine Prize for young scientists: Presidential Decree of Ukraine No. 595 / 2020 dated December 29, 2020. https://www.old.nas.gov.ua/UA/Messages/Pages/View.aspx?MessageID=7333

SCIENCE-BUSINESS CONNECTION

The GrantsForScience platform based on artificial intelligence technologies for cooperation between science and business. Grants for Science is a modern platform that creates a bridge between science and business. The platform provides personalized search for grant programs, partners, performers, allows creating consortia and managing projects, simplifying interaction among all participants.

Project description

Platform link: https://www.grantsforscience.com/

Scientific publications:

Oleksandr M. Khimich, Serhii V. Yershov, Elena A. Nikolaevskaya, Pavlo S. Yershov Development of an Intelligent Search System using GPT model for GrantsForScience platform. ProfIT AI 2024: 4th International Workshop of IT-professionals on Artificial Intelligence (ProfIT AI 2024), September 25–27, 2024, Cambridge, MA, USA. Vol-3777. P. 111-119 https://ceur-ws.org/Vol-3777/short3.pdf

Presentation videos:

International scientific project "Max-Planck-Gesellschaft zur Förderung der Wissenschaften", Max Planck Institute for Dynamics of Complex Technical Systems, (MPI-DCTS), Magdeburg, Germany (June 1, 2023 – May 31, 2026), O.M. Khimich, O.V. Popov, O.A. Nikolaevska, V.A. Sydoruk, O.V. Chistyakov, T.V. Chystiakova.

More details in the news

International Scientific Symposium "ISSUES OF COMPUTATION OPTIMIZATION (POO--XLVIII)", dedicated to the 100th anniversary of the birth of Academician V.M. Glushkov, September 19–22, 2023, Lviv, Ukraine.

Khymych O., Nikolaievska O., Baranov I. "Features of the use of multi-digit arithmetic in mathematical modeling" DOI: https://doi.org/10.15407/10.15407/fmmit2023.37.143

Popov O.V., Chistyakov O.V. "Reliability of computer solutions in the study of natural vibrations";

Duchenko O.S., Nesterenko A.N. "Application of mixed precision for solving systems of nonlinear equations by quasi-Newton methods".

Collection of reports: PHYSICO-MATHEMATICAL MODELING AND INFORMATION TECHNOLOGIES, (37)

International Scientific Conference "Actual Problems of Mechanics" (dedicated to the 145th anniversary of the birth of S.P. Tymoshenko), S.P. Tymoshenko Institute of Mechanics of the NAS of Ukraine, September 19–22, 2023, Kyiv, Ukraine

Khymych O.M., Nikolaievska O.A. Multi-digit arithmetic as a tool for obtaining reliable solutions of problems;

Khymych O.M., Popov O.V. Solving ill-posed problems with sparse matrix structures;

Sydoruk V.A., Chistyakov O.V., Pavlyuk A.V. Parallel algorithm of LDLT decomposition for mechanics problems;

Duchenko O.S., Nesterenko A.N. Modeling of planar curves using cubic curvature distribution/

International Scientific and Technical Conference "Automated Control Systems for Technological Processes and Moving Objects" (AVIA-2023), National Aviation University, April 18–20, 2023, Kyiv, Ukraine.

Syneglazov V.M., Khotyanivskyi V.P. "Machine learning in the problem of auto-calibration of moving elements of robotic systems on the example of stepper motor control"..

12th International Conference "IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications", September 7–9, 2023, Kyiv, Ukraine.

V. Syneglazov, O. Chumachenko, K. Lesohorskyi. Accuracy Improvement of Neural Networks Under Semi-Supervised Learning

International Scientific Conference "ISSUES OF COMPUTATION OPTIMIZATION (POO-XLIV)", dedicated to the 60th anniversary of the founding of the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kamianets-Podilskyi, September 26–29, 2017

Khymych O.M., Chistyakov O.V. Hybrid iterative subspace method algorithm for solving structural stability problems

XVIІ International Scientific and Technical Conference "ARTIFICIAL INTELLIGENCE AND INTELLIGENT SYSTEMS" (AIIS’2017), October 17–19, 2017, Kyiv, Ukraine

Khymych O.M., Popov O.V., Chystiakova T.V., Rudyich O.V., Chistyakov O.V. Intelligent system for research and solving eigenvalue problems on parallel computers with Intel Xeon Phi processors

International Scientific Conference dedicated to the 60th anniversary of the founding of the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine "MODERN INFORMATICS: PROBLEMS, ACHIEVEMENTS AND DEVELOPMENT PROSPECTS", Kyiv, December 13–15, 2017

Khymych O.M., Molchanov I.M., Popov O.V., Chystiakova T.V. Intelligent computer mathematics system for mathematical modeling on hybrid architecture computers

Chistyakov O.V. On the features of solving the algebraic eigenvalue problem on parallel computers with Intel Xeon Phi processors

Mikhalevich V.S., Bik, N.A. Brusnikin B.N.,…, Khimich A.N. et al. Numerical methods for the multiprocessor computing complex ES. / Edited by I.N. Molchanov. – Moscow: Publishing House of VVIA named after Prof. N.E. Zhukovsky, 1986, 401 p.
Khimich A.N., Molchanov I.N, Mova V.I. et al. Numerical software for MIMD computer Inparkom. – Kyiv: Naukova Dumka. – 2007. – 222 p.
Khimich A.N., Molchanov I.N., Popov A.V., Chistyakova T.V., Yakovlev M.F. Parallel algorithms for solving computational mathematics problems. – Kyiv: Naukova Dumka. – 2008. – 247 p.
Nikolaevskaja E.A., Chimich A.N, Chistyakova T.V. Programming with Multiple Precision. Springer-Verlag. Studies in Computational Intelligence, vol. 397, p. 233, Berlin, Heidelberg, 2012.
Khimich O.M., Petryk M.R., Mikhalyk D.M., Boyko I.V., Popov O.V., Sydoruk V.A. Methods of mathematical modeling and identification of complex processes and systems based on high-performance computing (neuro- and nanoporous cyber-physical systems with feedback, models with sparse structure data, parallel computations). Kyiv: National Academy of Sciences of Ukraine, V.M. Glushkov Institute of Cybernetics. 2021, 350 p.
V.O. Bohayenko, V.M. Bulavatskyi, O.M. Khimich. Mathematical and computer modeling in hydrogeomegration dynamics problems. "Naukova Dumka", Kyiv, Ukraine. 2022, 222 p.
Petryk M., Gancarczyk T., Khimich O. Methods of Mathematical Modeling and Identification of Complex Processes and Systems on the basis of High-performance Calculations (neuro- and nanoporous feedback cyber systems, models with sparse structure data, parallel computations). Scientific Publishing University of Bielsko-Biala. Bielsko-Biala, Poland 2021. 194 p.
Oleksandr M. Khimich, Ivan V. Sergienko, and Natalia A. Vareniuk. «Nova Science Publishers. Generalized Inverses: Algorithms and Applications». Chapter 7. Modeling Weighted Moore-Penrose Inverse with Indefinite Singular Weights. Edited by PhD Ivan Kyrchei, 2022, 41 p. DOI: https://doi.org/10.52305/MJVE4994 .
Khimich A.N., Nikolaevskaya E.A., Baranov I.A. «Matrix Theory – Classics and Advances». Weighted least squares perturbation theory. Edited by Dr. Mykhaylo Andriychuk. ISBN 978-1-80355-823-3, 2022, 3 p. DOI: https://doi.org/10.5772/intechopen.102885
Serhii Lupenko, Mykhaylo Petryk, André Pierre Legrand, Oleksandr Khimich. «High-Performance Technologies of Modeling and Identification of Complex Multi-Component Systems and Processes». Publishing House of the Opole University of Technology, 2024, p. 202. http://elartu.tntu.edu.ua/handle/lib/47577
Altenbach, H., Bogdanov, V., Grigorenko, A., Khimich, O., Kushnir, R., Nazarenko, V. (2024). Stages of Yaroslav M. Grigorenko’s Life Path and the Main Results of His Scientific Research. In: Altenbach, H., Bogdanov, V., Grigorenko, A.Y., Kushnir, R.M., Nazarenko, V.M., Eremeyev, V.A. (eds) Selected Problems of Solid Mechanics and Solving Methods. Advanced Structured Materials, vol 204. Springer, Cham. https://doi.org/10.1007/978-3-031-54063-9_1
Khimich, O., Popov, A. (2024). Solving Incorrect Problems of the Elasticity Theory. In: Altenbach, H., Bogdanov, V., Grigorenko, A.Y., Kushnir, R.M., Nazarenko, V.M., Eremeyev, V.A. (eds) Selected Problems of Solid Mechanics and Solving Methods. Advanced Structured Materials, vol 204. Springer, Cham. https://doi.org/10.1007/978-3-031-54063-9_19

2020-2024

Khimich, A.N., Nikolaevskaya, E.A. "Existence and Uniqueness of Weighted Normal Pseudosolutions," Cybernetics and Systems Analysis, 2020, 56(4), P, 544–549. https://doi.org/10.1007/s10559-020-00270-5
Petryk M.R., Boyko I.V., Khimich O.M., Petryk M.M. "High-performance supercomputer technologies for modeling nanoporous cybersystems with feedback for adsorption gas purification," Cybernetics and Systems Analysis, 2020, Vol 56(5), P. 835-847. https://doi.org/10.1007/s10559-020-00304-y-020-00304-y
O.M. Khimich, O.V. Popov, O.V. Chystyakov, V.A. Sidoruk, "A Parallel Algorithm for Solving a Partial Eigenvalue Problem for Block-Diagonal Bordered Matrices," Cybernetics and Systems Analysis, 2020, Volume 56, No. 6, pp. 61–74. https://doi.org/10.1007/s10559-020-00311-z
Khimich, A.N., Sydoruk, V.A., Nesterenko, A.N. "Hybrid algorithm Newton method for solving systems of nonlinear equations with block Jacobi matrix," CEUR Workshop Proceeding, 2020, V.2866, P. 209–217. https://www.scopus.com/authid/detail.uri?authorId=6602740665
Chikrii Al.A., Chikrii K.A. "On a Differential Game in a System Described by a Functional Differential Equation." Conference paper: "Stability, Control and Differential Games," (SCDG2020), Springer, 2020, P. 74–82. https://doi.org/10.1007/978-3-030-42831-0-6
Petryk M.R., Boyko I.V., Khimich O.M., Petryk M.M. "High-Performance Supercomputer Technologies of Simulation and Identification of Nanoporous Systems with Feedback for n-Component Competitive Adsorption," Cybernetics and Systems Analysis, 2021, 57(2), P. 316–328, https://doi.org/10.1007/s10559-021-00357-7
Khimich O.M., Chistyakova T.V., Sidoruk V.A., Yershov P.S. "Adaptive Computer Technologies for Solving Problems of Computational and Applied Mathematics," Cybernetics and Systems Analysis. 2021, 57(6), P. 990–997. https://doi.org/10.1007/s10559-021-00424-z
O. Khimich, A. Popov, A. Chistyakov. "Effective Use of Sparse Matrices in Problems of Mathematical Modeling." CEUR Workshop Proceeding, 2022, Vol. 3501, P. 212–221, Conference Paper. https://www.scopus.com/record/display.uri?eid=2-s2.0-85175705798&origin=resultslist + PDF
V. Sineglazov, K. Riazanovskiy, A. Klanovets, E. Chumachenko, N. Linnik. "Intelligent tuberculosis activity assessment system based on an ensemble of neural networks," Biology and Medicine, 2022, Vol. 147, P. 105800. https://doi.org 10.1016/j.compbiomed.2022.105800
Khimich O.M., Popov A.V. "Solving Ill-Posed Problems of the Theory of Elasticity Using High-Performance Computing Systems." Cybernetics and Systems Analysis, 2023, Vol. 59, No 5, P. 743–752. https://doi.org/10.1007/s10559-023-00610-1
Khimich O.M., Popov A.V., Chistyakov O.V., Kokhanovsky V.O. "Adaptive Algorithms for Solving Eigenvalue Problems in the Variable Computer Environment of Supercomputers." Cybernetics and Systems Analysis, 2023, Vol. 59, No 3, P. 480–492. https://doi.org/10.1007/s10559-023-00583-1
Petryk M. R., Boyko I.V., Khimich O.M., Sidoruk V.A. et al. "High-Performance Methods of Modeling the Nano-Adsorption and Diffusion with Feedback in Heterogeneous Cylindrical Multicomponent Nanoporous Media." Cybernetics and Systems Analysis, 2023, Vol. 59, No. 2, P. 1008–10222. https:doi/org/10.1007/s10559-023-00636-5
V. Sineglazov, K. Riazanovskiy, O. Klanovets. "A three-stage 2D–3D convolutional network ensemble for segmenting malignant brain tumors on MRI images." Cybernetics and Systems Analysis, 2023, Vol. 59, No. 2, P. 199–211. https://doi.org/10.1007/s10559-023-00555-5
Sineglazov, V., Chumachenko, O., Lesohorskyi, K. "Accuracy Improvement of Neural Networks Under Semi-Supervised Learning." Proceedings of the IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, IDAACS, 2023, P. 777–781. https://doi.org/10.1109/IDAACS58523.2023.10348869
Khotsianivskyi, V., Sineglazov, V. "Robotic manipulator motion planning method development using neural network-based intelligent system." Machinery and Energetics, 2023, 14(4), P. 131–145. https://doi.org/10.31548/machinery/4.2023.13
Sineglazov, V., Boryndo I. "Visual Navigation Systems Implementation Using Hybrid Convolutional Neural Networks." IEEE 7th International Conference on Methods and Systems of Navigation and Motion Control, MSNMC, Proceedings, 2023, P. 155–158. DOI: https://doi.org/10.1109/MSNMC61017.2023.10329122
Sineglazov, V., Lesohorskyi, K., Chumachenko, O. "Super-Resolution of Images Received from UA," IEEE 7th International Conference on Methods and Systems of Navigation and Motion Control, MSNMC 2023 – Proceedings, P. 159–162. https://doi.org/10.1109/MSNMC61017.2023.10329256
Sineglazov, V., Ryazanovskiy, K. "Object Detection and Classification Based on their 3D Models." 2023, IEEE 7th International Conference on Methods and Systems of Navigation and Motion. https://doi.org/10.1109/MSNMC61017.2023.10329099
Oleksandr Khimich, Serhii Yershov, Elena Nikolaevskaya, Pavlo Yershov. "Developing of an Intelligent Search Engine Using the GPT Model for the GrantsForScience Platform." CEUR Workshop Proceedings, Vol. 3777, P. 111 – 119, 2024, 4th International Workshop of IT-Professionals on Artificial Intelligence, ProfIT AI, Cambridge, 25–27 September. https://www.researchgate.net/publication/385653857_Development_of_an_Intelligent_Search_Engine_using_GPT_model_for_GrantsForScience_platform
Yurii Skob, Oleksandr Khimich, Oksana Pichugina, Andrii Hulianytskyi and Oleksii Kartasho. "Mathematical Modeling of Pressure Effects from Hydrogen Explosion." CEUR Workshop Proceedings. 2024, Vol. 3777, P. 282 – 299. 4th International Workshop of IT-Professionals on Artificial Intelligence, ProfIT AI, Cambridge, 25–27 September. https://grantsforscience.com/search?q=0000-0002-8103-4223
A. Kozhukhivskyi; O. Khimich; O. Potii; Y. Horbenko; O. Kozhuhivska; Y. Borsukovskiy. "Mathematical Foundations of Algebraic Lattices and Their Application in Quantum Cryptography." Ukrainian Information Security Research Journal, 2024, P. 117-129. https://doi.org/10.18372/2410-7840.26.18835
Zub S.S., Yalovega I.H., Lyashko S.I., Lyashko V. S. "Mathematical model of magnet superconducting suspension." Cybernetics and Systems Analysis, Vol. 60, No. 3, May, 2024. https://doi.org/10.1007/s10559-024-00679-2
Victor Sineglazov, Mykhailo Hordun, Samuli Junttila. "An intelligent system for determining the degree of tree bark beetle damage based on the use of generative-adversarial neural networks." Plant-Environment Interactions, 2024, 5(6). DOI: https://doi.org/10.1002/pei3.70015
Sineglazov, V., Ryazanovskiy, K., Sheruda, A. "Intelligent Infective Endocarditis Diagnostic System Based on Echocardiography." International Journal of Image, Graphics and Signal Processing, 2024, (5), P. 05–120. DOI: https://doi.org/10.5815/ijigsp.2024.05.08
Sineglazov, V., Lesohorskyi, K., Lytvynenko, V. "Intelligent hyperspectral image processing for landmine detection and classification." CEUR Workshop Proceedings, 3777, P. 40–51. https://www.scopus.com/record/display.uri?eid=2-s2.0-85210070674&origin=resultslist
Boryndo I., Sineglazov, V., Zgurovsky M.Z. "Multicriteria optimization of hybrid convolutional neural network structural synthesis using evolutionary algorithms." CEUR Workshop Proceedings, 3790, P. 318–330. https://www.scopus.com/record/display.uri?eid=2-s2.0-85207852127&origin=resultslist
Sineglazov V., Lesohorskyi K., Chumachenko O. "Faster Image Deblurring for Unmanned Aerial Vehicles." 2nd International Conference on Unmanned Vehicle Systems-Oman, UVS 2024. DOI: https://doi.org/10.1109/UVS59630.2024.10467152

2000-2023

Sergienko I.V., Khimich O.M. Mathematical modeling: From melm to exaflops. Bulletin of the NAS of Ukraine. 2019, No. 8, pp. 37–50. http://dspace.nbuv.gov.ua/handle/123456789/159894
Popov O.V. Rudich O.V. Chistyakov O.V. Multilevel model of parallel computations for linear algebra problems. Programming Problems. — 2018. — No. 2-3. — pp. 83-92. — Bibliography: 10 titles. — Ukr. http://dspace.nbuv.gov.ua/handle/123456789/144586
Khimich A.N., Dekret V.A., Popov A.V., Chistyakov O.V. Numerical Study of the Stability of Composite Materials on Computers of Hybrid Architecture. Journal of Automation and Information Sciences. 2018, 50 (7). Begell House Inc., pp. 7–24. DOI: 10.1007/s10559-020-00311-z.
Popov A.V., Khimich A.N., Chistyakov A.V. Parallel algorithm for solving the partial eigenvalue problem for block-diagonal matrices with bordering. Cybernetics and Systems Analysis, 2020. Vol. 56, No. 6, pp. 61–74. http://dspace.nbuv.gov.ua/handle/123456789/190515
Petryk M.R., Boyko I.V., Khimich O.M., Petryk M.M. "High-performance supercomputer technologies for modeling and identification of complex pressure cybernetic systems with feedback for n-component competitive adsorption" "Cybernetics and Systems Analysis", 2021, Vol. 57, No. 6, pp. 316–328. https://doi.org/10.1007/s10559-021-00357-7
Khimich O.M., Chistyakova T.V., Sydoruk V.A., Ershov P.S. Adaptive computer technologies for solving problems of computational and applied mathematics. Cybernetics and Systems Analysis, 2021, Vol. 57, No. 6, pp. 162–171. URL:http://www.kibernetika.
org/volumes/2021/numbers/06/NumberContentUA.html
Sydoruk V.A., Ershov P.S. Adaptive algorithm for solving systems of equations with block-skyscraper matrices. International Scientific and Technical Journal "Problems of Control and Informatics", 2022, Vol. 67, No. 5, pp. 17–31. DOI: https://doi.org/10.34229/2786-6505-2022-5-2
Khimich O.M., Popov A.V. "Solving Ill-Posed Problems of the Theory of Elasticity Using High-Performance Computing Systems". "Cybernetics and Systems Analysis", Vol. 59, No 5, 743–752, 2023, doi.org/10.1007/s10559-023-00610-1
Khimich O., Popov A., Chistyakov O., V. Kokhanovsky "Adaptive Algorithms for Solving Eigenvalue Problems in the Variable Computer Environment of Supercomputers" Cybernetics and Systems Analysis, Vol. 59, No 3, pp. 480–492, 2023, doi.org/10.1007/s10559-023-00583-1
O. Khimich, A. Popov, A. Chistyakov. Effective Use of Sparse Matrices in Problems of Mathematical Modeling. CEUR Workshop Proceedings (CEUR-WS.org), 2023, Proceedings (CEUR-WS.org), 2023
V. Sineglazov, K. Riazanovskiy, O. Klanovets "A three-stage 2D–3D convolutional network ensemble for segmenting malignant brain tumors on MRI images." "Cybernetics and Systems Analysis", 2023, Vol. 59, No. 2, pp. 199–211, 2023, doi.org/10.1007/s10559-023-00555-5
M.R. Petryk, I.V. Boyko, O.M. Khimich, V.A. Sydoruk. High-performance methods for modeling nanoabsorption and diffusion with feedback in heterogeneous cylindrical multicomponent nanoporous media. Cybernetics and Systems Analysis, 2023, Vol. 59, No. 6, pp. 163–177.

A methodology for researching and calculating mathematical models described by problems with a unique solution in a subspace (conditionally well-posed problems) has been developed and justified, using the normal pseudoinverse solution of SLAE of a discrete finite element model. A three-stage regularization method has been proposed for computing the pseudoinverse solution with a predetermined accuracy. The methodology is implemented for the first main problem of elasticity theory using a hybrid parallel computation model, invariant for a wide class of problems with Neumann boundary conditions. It can be applied for the numerical solution of boundary value problems that have a unique solution in a subspace for mathematical modeling in various fields of science, engineering, etc. There is no analogous methodology for this class of problems in global practice.
The theoretical foundations and new block algorithms for high-performance computing using multi-precision arithmetic have been developed for researching and solving linear algebra problems (systems of linear algebraic equations, algebraic eigenvalue problems) on heterogeneous computers. The use of multi-precision arithmetic in solving linear algebra problems ensures the necessary reliability of calculation results. Such algorithms can be applied to a wide range of mathematical modeling problems, including the calculation of frequencies and modes of natural vibrations for studying the condition of damaged building structures and facilities.
New algorithms using mixed precision have been developed for solving linear algebra problems and systems of nonlinear equations arising in mathematical modeling. The use of mixed precision helps reduce the computational time while maintaining solution accuracy. These algorithms can be applied in the calculations of mathematical models, for example, in studies of the life cycle of welded structures, the condition of damaged buildings, etc.
An intelligent interface for computer modeling of physico-mechanical processes has been developed, implementing an innovative approach to automating modeling with approximate data and sparse output data of large volumes on an efficient parallel computing model, using hybrid artificial intelligence tools (combining neural network technologies and formal knowledge representation), with guaranteed reliability of results. On the SKIT cluster complex, intelligent interfaces have been software-implemented for modeling the condition and predicting the lifespan of critical welded structures and for computer research of the stability of new composite materials. A significant improvement in the efficiency of mathematical modeling has been achieved.
Effective methods for forming training samples based on the study of self-learning methods, including methods for labeling unlabeled data and wrapper methods, have been developed. Classes and possible training datasets for optimizing neural network tuning using semi-supervised learning methods have been identified. A classification based on the number of classifiers used and their types has been developed (based on the study of wrapper methods and highlighting their advantages). The obtained results can be used in building artificial intelligence systems in various fields of science and engineering and implemented, in particular, in the medical and military sectors.

Dear colleagues! At this difficult time for the our country and science, we offer topics for cooperation:

Adaptive algorithms for high-performance computing for mathematical modeling of physical and technical processes in a changing computer environment.
Intelligent interface for modeling physical and mechanical processes based on parallel computing
Methods and algorithms of hybrid semi-controlled learning of neural networks in artificial intelligence problems
Intelligent image processing system of high accuracy, in the presence of noise
High-performance calculations: models, methods, applications

We are waiting for suggestions!

Scientific conferences and seminars co-organized by the department staff:

International Symposium "Issues of Computation Optimization" (Leaders: Academician of NAS of Ukraine V.K. Zadyraka, Academician of NAS of Ukraine O.M. Khimich)
International Scientific Seminar "Quantum Computing" (Leaders: Academician of NAS of Ukraine V.K. Zadyraka, Academician of NAS of Ukraine O.M. Khimich)
Scientific Seminar "Methods of Computational Mathematics" (Leaders: Academician of NAS of Ukraine V.K. Zadyraka, Academician of NAS of Ukraine O.M. Khimich)

Popov Oleksandr Volodymyrovych, acting head of department, senior researcher, Doctor of Physical and Mathematical Sciences, senior researcher,
tel.: +38 (044) 526 11 96, e-mail: dept150@insyg.kiev.ua.

Khimich Oleksandr Mykolayovych , chief researcher, academician of NAS of Ukraine, Doctor of Physical and Mathematical Sciences, professor.
tel.: +38 (044) 526 60 88, e-mail: khimich505@gmail.com

Nikolaievska Olena Anatoliyivna, senior researcher, Candidate of Physical and Mathematical Sciences,
tel.: +38 (044) 526 11 96, e-mail: dept150@insyg.kiev.ua

Sydoruk Volodymyr Antonovych, senior researcher, Candidate of Physical and Mathematical Sciences,
tel.: +38 (044) 526 11 96, e-mail: wolodymyr.sydoruk@gmail.com

Chystiakov Oleksii Valeriyovych senior researcher, Candidate of Physical and Mathematical Sciences,
tel.: +38 (044) 526 11 96, e-mail: Alexej.Chystyakov@gmail.com

Chystiakova Tamara Vasylivna, senior researcher, Candidate of Physical and Mathematical Sciences, senior researcher,
tel.: +38 (044) 526 11 96, e-mail: tamara.chystjakova@gmail.com

Baranov Ihor Anatoliyovych, researcher,
tel.: +38 (044) 526 11 96, e-mail: vlasov@ukr.net

Duchenko Oleksandr Serhiyovych, junior researcher,
tel.: +38 (044) 526 11 96, e-mail: dept150@insyg.kiev.ua

Nesterenko Alla Nykyforivna, junior researcher,
tel.: +38 (044) 526 11 96, e-mail: alla.nest1958@gmail.com

Avdeienko Liliya Mykhailivna, engineer-programmer of the 1st category
tel.: +38 (044) 526 11 96, e-mail: dept150@insyg.kiev.ua

Department of Numerical Methods and Computer Modeling

Oleksandr M. Khimich

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