Application of feedforward neural network in the study of dissociated gas flow along the porous wall

This paper concerns the use of feedforward neural networks (FNN) for predicting the nondimensional velocity of the gas that flows along a porous wall. The numerical solution of partial differential equations that govern the fluid flow is applied for training and testing the FNN. The equations were solved using finite differences method by writing a FORTRAN code. The Levenberg-Marquardt algorithm is used to train the neural network. The optimal FNN architecture was determined. The FNN predicted values are in accordance with the values obtained by the finite difference method (FDM). The performance of the neural network model was assessed through the correlation coefficient (r), mean absolute error (MAE) and mean square error (MSE). The respective values of r, MAE and MSE for the testing data are 0.9999, 0.0025 and 1.9998.10^-^5.

[1]  Mohammad Bagher Menhaj,et al.  Training feedforward networks with the Marquardt algorithm , 1994, IEEE Trans. Neural Networks.

[2]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[3]  Miguel Pinzolas,et al.  Neighborhood based Levenberg-Marquardt algorithm for neural network training , 2002, IEEE Trans. Neural Networks.

[4]  Jennie Si,et al.  Advanced neural-network training algorithm with reduced complexity based on Jacobian deficiency , 1998, IEEE Trans. Neural Networks.

[5]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[6]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[7]  Siwei Luo,et al.  Numerical solution of elliptic partial differential equation using radial basis function neural networks , 2003, Neural Networks.

[8]  Ali Reza Tahavvor,et al.  Natural cooling of horizontal cylinder using Artificial Neural Network (ANN) , 2008 .

[9]  Luo Siwei,et al.  Numerical solution of elliptic partial differential equation using radial basis function neural networks. , 2003, Neural networks : the official journal of the International Neural Network Society.

[10]  James J. Carroll,et al.  Approximation of nonlinear systems with radial basis function neural networks , 2001, IEEE Trans. Neural Networks.

[11]  H. P. Kreplin,et al.  Grenzschicht-Theorie , 1983 .

[12]  Zhi Shang,et al.  Application of artificial intelligence CFD based on neural network in vapor-water two-phase flow , 2005, Eng. Appl. Artif. Intell..

[13]  Abdullatif Ben-Nakhi,et al.  Neural networks analysis of free laminar convection heat transfer in a partitioned enclosure , 2007 .

[14]  R. Glowinski,et al.  Partial differential equations : modeling and numerical simulation , 2008 .

[15]  Engin Avci,et al.  Analysis of adaptive-network-based fuzzy inference system (ANFIS) to estimate buoyancy-induced flow field in partially heated triangular enclosures , 2008, Expert Syst. Appl..

[16]  H. S. M. Beigi,et al.  Learning algorithms for neural networks based on Quasi-Newton methods with self-scaling , 1993 .

[17]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

[18]  Michael Schäfer,et al.  Bayesian regularization neural networks for optimizing fluid flow processes , 2006 .

[19]  Konrad Reif,et al.  Multilayer neural networks for solving a class of partial differential equations , 2000, Neural Networks.

[20]  Y. Varol,et al.  Prediction of flow fields and temperature distributions due to natural convection in a triangular enclosure using Adaptive-Network-Based Fuzzy Inference System (ANFIS) and Artificial Neural Network (ANN) , 2007 .

[21]  Nameer N. El-Emam,et al.  An intelligent computing technique for fluid flow problems using hybrid adaptive neural network and genetic algorithm , 2011, Appl. Soft Comput..

[22]  Mohsen Hayati,et al.  Multilayer perceptron neural networks with novel unsupervised training method for numerical solution of the partial differential equations , 2009, Appl. Soft Comput..