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Use of artificial neural networks as explicit finite difference operators

journal contribution
posted on 2005-10-01, 00:00 authored by Lloyd ChuaLloyd Chua, S Tan
Results of a numerical exercise, substituting a numerical operator by an artificial neural network (ANN) are presented in this paper. The numerical operator used is the explicit form of the finite difference (FD) scheme. The FD scheme was used to discretize the one-dimensional transport equation, which included both the advection and dispersion terms. Inputs to the ANN are the FD representation of the transport equation, and the concentration was designated as the output. Concentration values used for training the ANN were obtained from analytical solutions. The numerical operator was reconstructed from a back calculation of the weights of the ANN. Linear transfer functions were used for this purpose. The ANN was able to accurately recover the velocity used in the training data, but not the dispersion coefficient. This capability was improved when numerical dispersion was taken into account; however, it is limited to the condition: C/P<0.5 , where C is the Courant number and P , the Peclet number (i.e., the restriction imposed by the Neumann stability condition).

History

Journal

Journal of computing in civil engineering

Volume

19

Pagination

426-429

Location

Reston, Va.

ISSN

0887-3801

Language

eng

Publication classification

C2.1 Other contribution to refereed journal

Copyright notice

2005, ASCE

Issue

4

Publisher

American Society of Civil Engineers