Multilayer neural network models based on grid methods

11th International Conference on "Mesh methods for boundary-value problems and applications"

Lazovskaya, T.^1 ; Tarkhov, D.^1

Peter the Great St-Petersburg Polytechnic University, 29 Politechnicheskaya Str, Saint-Petersburg

195251, Russia^1

关键词: Classic models;    Classical schemes;    Continuous approximations;    Hybrid model;    Non-linear relationships;    Numerical experiments;    Ordinary and partial differential equations;    Simple modifications;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012061/pdf
DOI  :  10.1088/1757-899X/158/1/012061

来源: IOP

【 摘 要 】

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.