Neural network as an approximator of a dynamic system

Mathematical modeling allows us to describe the processes taking place around us in the language of mathematical formulas. For example, the change in predator and prey populations during interaction in nature is described by the Lotka–Volterra equation. Of course, the theoretical model will always be some approximation to the true behavior and real processes occurring in nature. The degree of error is a key characteristic of mathematical models. There are crude models that take into account only the basic qualities and characteristics of the system, and there are models that build a more accurate forecast. The inclusion in the model equation of the corresponding terms describing certain qualities of the process will be a way to refine the model. The question of the selection of these terms is solved in each case individually. In this paper, we propose an approach to refine the rough model by including a function such as an artificial neural network, for the description of which a sufficient data set is required.