CONSTRUCTION OF ANALYTICAL MODELS OF VARIOUS PHYSICAL AND CHEMICAL SYSTEMS BY METHODS OF DATA SCIENCE
AND MATHEMATICAL PROTOTYPING OF ENERGY PROCESSES 

Igor E. Starostin, Doctor of technical sciences, professor, professor of the sub-department of electrical engineering and aviation electrical equipment, Moscow State Technical University of Civil Aviation (20 Kronshtadtskiy boulevard, Moscow, Russia), starostinigo@yandex.ru

Background. Construction of mathematical models of systems of various physical and chemical nature is the most important stage in the development of methods for designing and operating the above-mentioned systems. Currently, there are Data Science methods dedicated to collecting and processing data with subsequent construction of mathematical models. To construct the above-mentioned models, it is necessary to specify their class. The main requirements for mathematical models of systems of various physical and chemical nature are their accuracy and adequacy (consistency with physical and chemical laws). To construct a class of mathematical models of the above-mentioned systems that satisfy the above-mentioned requirements, a method of mathematical prototyping of energy processes was proposed within the framework of mechanics, electrodynamics and modern non-equilibrium thermodynamics. In accordance with the above-mentioned method, complete mathematical models of various physical and chemical systems with an accuracy of up to experimentally studied constant coefficients can be obtained in the form of a system of differential equations. Then, the obtained complete models are transformed into simplified analytical models with an accuracy of up to constant coefficients, which are trained on experimental data. This work is devoted to the methodology of constructing models applicable for solving practical problems based on Data Science methods and the method of mathematical prototyping of energy processes. Matherials and methods. Synthesis in the form of differential equations of a complete model of the dynamics of physical and chemical processes is carried out on the basis of the method of mathematical prototyping of energy processes and methods of dynamic programming. Construction of simplified analytical models applicable to solving practical problems is carried out by means of a computational experiment based on a complete model with further application of methods of identification, symbolic regression, machine learning. Results. The proposed methodology allows to build accurate and adequate models applicable for solving practical problems within acceptable timeframes. Conclusions. The proposed methodology for constructing mathematical models can be used as the basis for a software and technology platform for digital twins that consumes acceptablecomputing resources.

method of mathematical prototyping of energy processes, Data Science, machine learning, dynamic programming

Starostin I.E. Construction of analytical models of various physical and chemical systems by methods of Data Science and mathematical prototyping of energy processes. Nadezhnost' i kachestvo slozhnykh sistem = Reliability and quality of complex systems. 2025;(3):36–44. (In Russ.). doi: 10.21685/2307-4205-2025-3-4