Let it need to be solved the inverse problem of mathematical modelling for a process characterized by an arbitrary number of input and output variables, i.e., build a model in the form of a system of differential equations according to the measurements of inputs and outputs: The paper analyzes a method based on a self-configuring genetic programming algorithm for identification of dynamic systems with input effects changing according to predetermined laws. Systems of differential equations are applied to represent such processes. It is worth noting that they often contain not one, but several output characteristics when studying manufacturing processes. In this aspect, it is necessary to take into account the interpretability of the obtained results provided by the symbolic representation of differential equations. The representation in the form of differential equations makes it possible to obtain a model that is suitable for further study. The study of a wide range of problems connected with the strength of materials, biology, economics shows that their solution is reduced to mathematical modeling in the form of a functional dependence described by differential equations and their systems. Differential equations and their systems can be applied as a tool for modeling various phenomena in mechanics, chemical reactions, electrical and magnetic phenomena ( Escalante-MartĂnez et al., 2020). The theory of differential equations is characterized by its direct application for practical problems ( Chu & Marynets, 2021). It is extremely important for the development of various branches of science and technology ( Brester & Ryzhikov, 2019 Liu et al., 2021). They are functionally applied in manufacturing. Differential equations and their systems are the basis for studying in the mathematical modeling field. They are the basis of differential equations. An analytical representation of such changes are derivatives. The study of various systems’ behavior often leads to analysis and solution of equations that include characteristics such as a rate of change of system parameters. These methods belong to the analytical and numerical, parametric and nonparametric classes ( Brester et al., 2020 Ovcharenko, 2020 Roehrl et al., 2020). A lot of methods have been developed to simulate dynamic processes. Mathematical modeling of dynamic systems is an interdisciplinary tool for studying various processes in nature, society and industry. Keywords: Differential equation, identification, evolutionary algorithms Introduction The obtained results prove efficiency of the developed method under various input influences. It demonstrates graphical interpretation of the obtained results. The conducted study takes into account the presence of noise in the initial samples. The presented paper studies efficiency of the proposed method on five problems where the initial objects are represented by systems of differential equations of various orders. The method performs self-configuring of parameters for evolutionary algorithms. Genetic programming and differential evolution are the algorithmic basis of the method. The paper studies the efficiency of the method based on evolutionary algorithms to identify objects in the form of systems of differential equations with various input effects. A change in the input action according to a predetermined law could be one of features for dynamic processes. However, as processes become more complex, there exist a need to develop new tools. Therefore, a great number of methods for dynamical systems identification have been developed. Objects from different areas are dynamic. Nowadays, differential equations and their systems are one of the most preferred ways to represent models of dynamic objects.
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