SOFTWARE ENVIRONMENT FOR IDENTIFICATION OF NONLINEAR MATHEMATICAL MODELS USING OPTIMIZATION PROCEDURES

Bohdan Melnyk

Abstract


Background. For an adequate description of complex systems, it is necessary to use significantly nonlinear mathematical models. An effective approach to the identification of such models is the use of optimization procedures based on various optimization methods. For the comprehensive implementation of these procedures, it is necessary to create software that meets modern trends in the field of computer modeling.

Materials and Methods. To identify models, various optimization algorithms are used, which are developed within the framework of various optimization methods, in particular, within the framework of quasi-Newton methods or stochastic methods. The article considers the BFGS, L-BFGS, and L-BFGS-B algorithms, which belong to the first class of methods, and algorithms that implement the stochastic directed cone method, namely: the basic algorithm and its three modifications. A researcher engaged in mathematical modeling selects one of the software-implemented optimization algorithms that best corresponds to the formulated modeling problem. To do this, he must be able to evaluate the qualitative indicators of these algorithms, which are integrated in a single software environment.

Results and Discussion. The software environment for the identification of mathematical models using optimization procedures, in addition to the specific features associated with identification, must comply with modern programming paradigms and their use. In view of this, it is proposed to use the Python programming environment for its creation. The structure of the software subsystem that implements the selection of the type of mathematical model, its structural and parametric identification and evaluation, as well as integration with other subsystems of the created software environment, is considered. General requirements for ensuring its functionality are formulated. The prospects for the application of cloud IT and AI are considered.

Conclusion. The proposed software and architectural solutions allow creating a software environment that will significantly facilitate the process of computer-generated mathematical models of various complex systems. At the same time, it remains open for further modernization and expansion of functionality.

Keywords: mathematical model, identification, optimization algorithms, software, architecture.


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References


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DOI: http://dx.doi.org/10.30970/eli.34.10

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