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Information × Registration Number 0223U004379, 0121U110612 , R & D reports Title Methods of high-performance computing for the study of mathematical models of complex dynamical systems popup.stage_title Head Makarov Volodymyr L., Доктор фізико-математичних наук Registration Date 24-10-2023 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2  The object of research is machine learning problems, problems of liquid oscillations in tanks with a free surface, diffusion mapping, parallel calculation methods. The purpose of the second stage of the project is to develop modified methods of diffusion mapping and corresponding algorithms, which are fundamentally more efficient from a computational point of view and, as a result, can be applied to solving machine learning problems in the case of large and super-large objects. by the set of input data; development and substantiation of parallel numerical methods of approximation of matrix functions that fully take into account available a priori information about the spectrum of generators of diffusion processes; development and justification of effective algorithms for ranking problems; establishing the optimal approximation accuracy for the developed algorithms in the case of smooth solutions; Research methods - methods of functional analysis, methods of theory of functions, methods of semi-group theory, numerical methods, methods of approximation theory, methods of theory of ordinary differential equations, methods of solving eigenvalue problems, methods of mathematical modeling. Within the framework of the second stage of research work, a wide range of problems arising in the theory of machine learning methods were solved. In particular, a strategy for solving machine learning problems using the Hilbert space of the reproducible kernel has been developed, and machine learning methods for solving domain adaptation problems have been developed. Machine learning methods based on diffusion geometry are proposed for solving handwritten text processing problems. A machine learning technique is proposed to obtain damping rate functions in the so-called single dominant modal system describing a resonant liquid splashing in a rectangular tank. An exponentially convergent method for solving the problem with a fractional derivative and an unbounded operator coefficient. Product Description popup.authors Vasylyk Vitalii Bogdanovych Sytnyk Dmytro Oleksiyovych Solodky Sergiy Grygorovych Tymokha Oleksandr Mykolayovych popup.nrat_date 2023-10-24 Close