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Some methods of training radial basis neural networks in solving the Navier‐Stokes equations
Author(s) -
Sinchev Bakhtgerey,
Sibanbayeva Saulet Erbulatovna,
Mukhanova Axulu Mukhambetkaliyevna,
Nurgulzhanova Assel Nurgulzhanovna,
Zaurbekov Nurgali Sabyrovich,
Imanbayev Kairat Sovetovish,
Gagaridezhda Lvovna,
Baibolova Lyazzat Kemerbekovna
Publication year - 2017
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4470
Subject(s) - artificial neural network , radial basis function , basis (linear algebra) , basis function , navier–stokes equations , partial differential equation , differential equation , mathematics , computer science , representation (politics) , gaussian , algorithm , mathematical optimization , artificial intelligence , mathematical analysis , geometry , physics , quantum mechanics , politics , compressibility , political science , law , thermodynamics
Summary The purpose of this research is to analyze the application of neural networks and specific features of training radial basis functions for solving 2‐dimensional Navier‐Stokes equations. The authors developed an algorithm for solving hydrodynamic equations with representation of their solution by the method of weighted residuals upon the general neural network approximation throughout the entire computational domain. The article deals with testing of the developed algorithm through solving the 2‐dimensional Navier‐Stokes equations. Artificial neural networks are widely used for solving problems of mathematical physics; however, their use for modeling of hydrodynamic problems is very limited. At the same time, the problem of hydrodynamic modeling can be solved through neural network modeling, and our study demonstrates an example of its solution. The choice of neural networks based on radial basis functions is due to the ease of implementation and organization of the training process, the accuracy of the approximations, and smoothness of solutions. Radial basis neural networks in the solution of differential equations in partial derivatives allow obtaining a sufficiently accurate solution with a relatively small size of the neural network model. The authors propose to consider the neural network as an approximation of the unknown solution of the equation. The Gaussian distribution is used as the activation function.