The paper is devoted to the urgent task of developing a more informative nonlinear forecast with the highest degree of adequacy to the real process, although the mathematical apparatus of this process is not sufficiently developed. The search for types of relationships between two or more variables is performed using mathematical methods of processing the results of observations. This approach is used to simplify complex functions for analysis, modeling, and computation, as well as for forecasting and decision making in various fields, including science and mathematics, physics and engineering, machine learning, economics and finance, and others. Approximation allows calculating numerical characteristics and studying the qualitative properties of complex data for data analysis. The method simplifies complex theoretical information to suit practical problems for building models.