Construction of a Neural Network Semi-empirical Model of Deflection of a Sample from a Composite Material

Abstract

In the course of this work, experiments were carried out to simulate the deflection of the composite tape between two supports under the action of gravity without load and under load. The position was approximated during deformation of a given object accounting its individual properties. As an example of this problem, we proposed an approach that allows us to take into account the individual features of a real object without complicating the differential structure of the model using real measurements. The differential model itself describes a narrow class of objects that are similar in some properties and can give a poor forecasting result for specific real objects. Accounting measurements allows extremely well consider the individual characteristics of the simulated object without complicating the differential structure. In the proposed neural network approach, the loss function is composed so that to take into account the differential structure, boundary conditions, and measurement data. The loss function is represented as a sum, each term of which is a weighted functional. One functional is responsible for satisfying the differential structure of the model, another for boundary conditions, and a third for the quality of the description of real measurements. The role of the weights is to align of all terms in a series. The application of global minimum search methods for such a loss function allows one to obtain reliable results even in the case of using an unsuitable differential model.