Comparative analysis of hybrid neural network and multilayer modeling the deflection of a circular membrane under the action of a load located asymmetrically relatively to its center

This article is devoted to the problem of a hybrid approach in modelling, which combines methods based on mathematical physics equations and data-driven methods. The issue of choosing a hybrid model for circular membrane deflection under a load is considered. To build models, the Laplace equation inaccurately describing the object and measurement data of sufficiently high accuracy are used. With the help of cross-validation methods, an algorithmic comparison of the generalising ability of a multilayer model, a physics informed neural network model and a classical approach is made. The results obtained allow us to recommend neural network and multilayer methods for modelling objects when a sufficiently accurate classical description using a boundary value problem is unknown or excessively difficult and additional information is available in the form of measurement results. Multilayer methods are preferable in case of shortage of data or its dynamic nature, if a compact adaptive model is needed, including for use in embedded systems and digital twins.