Multilayer neural network models based on grid methods

The article discusses building hybrid models relating classical numerical methods for solving ordinary and partial differential equations and the universal neural network approach being developed by D Tarkhov and A Vasilyev. The different ways of constructing multilayer neural network structures based on grid methods are considered. The technique of building a continuous approximation using one simple modification of classical schemes is presented. Introduction non-linear relationships into the classic models with and without posterior learning are investigated. The numerical experiments are conducted.