The method of successive approximations for constructing a model of dynamic polynomial regression

Predicting the behavior of a certain process in time is an important task that arises in many applied areas, and information about the system that generated this process can either be completely absent or be partially limited. The only available knowledge is the accumulated data on past states and process parameters. Such a task can be successfully solved using machine learning methods, but when it comes to modeling physical experiments or areas where the ability of a model to generalize and interpretability of predictions are important, then the most machine learning methods do not fully satisfy these requirements. The forecasting problem is solved by building a dynamic polynomial regression model, and a method for finding its coefficients is proposed, based on the connection with dynamic systems. Thus, the constructed model corresponds to a deterministic process, potentially described by differential equations, and the relationship between its parameters can be expressed in an analytical form. As an illustration of the applicability of the proposed approach to solving forecasting problems, we consider a synthetic data set generated as a numerical solution of a system of differential equations that describes the Van der Pol oscillator.