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Information × Registration Number 0221U107125, 0120U104004 , R & D reports Title Complex dynamical systems in the sciences: theory, mathematical modelling, computing and application to advanced technology popup.stage_title Head Timokha Oleksandr M., Доктор фізико-математичних наук Registration Date 27-12-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 Res. object: Complex dynamic systems for sloshing and methods on machine learning; evolutionary boundary value problems. Purpose: Generalization of machine learning methods of the liquid sloshing mathematical models to account for dissipative and nonlinear physical phenomena. Investigation of the qualitative behavior of evolutionary boundary value problems, getting the necessary and sufficient conditions for the existence of bounded solutions along the entire axis in the Banach and Hilbert spaces, construction of the solvability theory and bifurcation conditions for the solutions. Methods: Machine learning and mathematical modeling, bifurcation theory, asymptotic methods of nonlinear mechanics, apparatus of generalized-inverted and pseudo-inverted operators, etc. Results and novelty: first: – methods of the hidden physics by the machine learning (due to the small amount of experimental data) of nonlinear adaptive modal models that describe sloshing are proposed; this made it possible to account for the nonlinear dissipative phenomena in the mechanical system; – the necessary and sufficient conditions for the existence of bounded (on the whole axis) solutions of boundary value problems for evolution equations in Banach and Hilbert spaces under the condition of exponential dichotomy on the axes of the corresponding homogeneous equation are obtained, boundary value problems with impulse influence are studied, the theory of solvability and conditions of bifurcation of solutions of evolutionary boundary value problems is constructed. Impl. of the results: The project is theoretical; it does not suggests creating scientific and technical products. Keywords: Machine learning; nonlinear modal system; sloshing; evolution equations; operator-differential equation; Green operator. Product Description popup.authors Bondar Ivanna A. Burylko Oleksandr А. Vasylyk Vitalii Bogdanovych Lahodzinskyi Oleksandr Ye Lokaziuk Oleksandra V Pokutnyi Oleksandr O Raynovskyy Ihor A Satur Oksana R Timokha Olexander M popup.nrat_date 2022-03-09 Close