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- W2067897195 abstract "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)." @default.
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- W2067897195 date "2005-10-01" @default.
- W2067897195 modified "2023-10-14" @default.
- W2067897195 title "Use of Artificial Neural Networks as Explicit Finite Difference Operators" @default.
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- W2067897195 doi "https://doi.org/10.1061/(asce)0887-3801(2005)19:4(426)" @default.
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