caa a22 4500 606159851 CHVBK 20210128100627.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s00521-014-1762-2 doi (NATIONALLICENCE)springer-10.1007/s00521-014-1762-2 Artificial neural network method for solving the Navier-Stokes equations [Elektronische Daten] [M. Baymani, S. Effati, H. Niazmand, A. Kerayechian] In this paper, a new method based on neural network is developed for obtaining the solution of the Navier-Stokes equations in an analytical function form. The solution procedure is based upon forming a trial solution consisting of two parts. The first part directly satisfies the boundary conditions and therefore, contains no adjustable parameters. The second part is constructed such that the governing equation is satisfied inside the solution domain, while the boundary conditions remain untouched. This part involves a feed-forward neural network, containing adjustable parameters (the weights), which must be determined such that the resulting approximate error function is minimized. The details of the method are discussed, and the capabilities of the method are illustrated by solving Navier-Stokes problem with different boundary conditions. The performance of the method and the accuracy of the results are evaluated by comparing with the available numerical and analytical solutions. The Natural Computing Applications Forum, 2014 Numerical solutions nationallicence Artificial neural network nationallicence Navier-Stokes equations nationallicence Baymani M. Department of Mathematics, Quchan University of Advanced Technology, Quchan, Iran aut Effati S. Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran aut Niazmand H. Mechanical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran aut Kerayechian A. Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran aut Neural Computing and Applications Springer London 26/4(2015-05-01), 765-773 0941-0643 26:4<765 2015 26 521 https://doi.org/10.1007/s00521-014-1762-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00521-014-1762-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Baymani M. Department of Mathematics, Quchan University of Advanced Technology, Quchan, Iran aut NATIONALLICENCE 700 1- Effati S. Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran aut NATIONALLICENCE 700 1- Niazmand H. Mechanical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran aut NATIONALLICENCE 700 1- Kerayechian A. Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran aut NATIONALLICENCE 773 0- Neural Computing and Applications Springer London 26/4(2015-05-01), 765-773 0941-0643 26:4<765 2015 26 521