Journal of Engineering and Applied Sciences
Year:
2019
Volume:
14
Issue:
23
Page No.
8576 - 8584
Neural network, differential equation, PSO algorithm, sensitivity, adjustable, convergnece
Authors :
Saadat Behzadi
and
Maliheh Miri
References
Angeline, P.J., G.M. Saunders and J.B. Pollack, 1994. An evolutionary algorithm that constructs recurrent neural networks. IEEE. Trans. Neural Netw., 5: 54-65.
CrossRef | Direct Link | Fasshauer, G.E., 1999. Solving differential equations with radial basis functions: Multilevel methods and smoothing. Adv. Comput. Math., 11: 139-159.
CrossRef | Direct Link | Franke, C., 1998. Solving partial differential equations by collocation using radial basis functions. Appl. Math. Comput., 93: 73-82.
CrossRef | He, S., K. Reif and R. Unbehauen, 2000. Multilayer neural networks for solving a class of partial differential equations. Neural Netw., 13: 385-396.
CrossRef | PubMed | Direct Link | Jianyu, L., L. Siwei, Q. Yingjian and H. Yaping, 2002. Numerical solution of differential equations by radial basis function neural networks. Proceedings of the 2002 International Joint Conference on Neural Networks (IJCNN’02) (Cat. No.02CH37290) Vol. 1, May 12-17, 2002, IEEE, Honolulu, Hawaii, USA., pp: 773-777.
Kennedy, J. and R. Eberhart, 1995. Particle swarm optimization. Proceedings of the IEEE International Conference on Neural Networks (ICNN’95) Vol. 4, November 27-December 01, 1995, IEEE, Perth, Western, ISBN:0-7803-2768-3, pp: 1942-1948.
Koh, C.S., O.A. Mohammed and S.Y. Hahn, 1994. Detection of magnetic body using artificial neural network with modified simulated annealing. IEEE. Trans. Magn., 30: 3644-3647.
CrossRef | Direct Link | Lagaris, I.E., A. Likas and D.I. Fotiadis, 1998. Artificial neural networks for solving ordinary and partial differential equations. IEEE. Trans. Neural Netw., 9: 987-1000.
CrossRef | Direct Link | Lee, H. and I.S. Kang, 1990. Neural algorithm for solving differential equations. J. Comput. Phys., 91: 110-131.
CrossRef | Direct Link | Meade Jr, A.J. and A.A. Fernandez, 1994. Solution of nonlinear ordinary differential equations by feedforward neural networks. Math. Comput. Modell., 20: 19-44.
CrossRef | Direct Link | Meade Jr., A.J. and A.A. Fernandez, 1994. The numerical solution of linear ordinary differential equations by feedforward neural networks. Math. Comput. Modell., 19: 1-25.
CrossRef | Direct Link | Parisi, D.R., M.C. Mariani and M.A. Laborde, 2003. Solving differential equations with unsupervised neural networks. Chem. Eng. Process. Process Intensif., 42: 715-721.
CrossRef | Direct Link | Perng, M.H., 1986. Direct approach for the optimal control of linear time-delay systems via shifted legend re polynomials. Intl. J. Control, 43: 1897-1904.
CrossRef | Direct Link | Puffer, F., R. Tetzlaff and D. Wolf, 1995. A learning algorithm for Cellular Neural Networks (CNN) solving nonlinear partial differential equations. Proceedings of the International Symposium on Signals, Systems and Electronics (ISSE’95), October 25-27, 1995, IEEE, San Francisco, California, USA., pp: 501-504.
Ramuhalli, P., L. Udpa and S.S. Udpa, 2005. Finite-element neural networks for solving differential equations. IEEE. Trans. Neural Netw., 16: 1381-1392.
CrossRef | Direct Link | Razzaghi, M. and M. Shafiee, 1998. Optimal control of singular systems VIA legendre series. Intl. J. Comput. Math., 70: 241-250.
CrossRef | Direct Link | Shaw, D. and W. Kinsner, 1996. Chaotic simulated annealing in multilayer feedforward networks. Proceedings of the 1996 Canadian Conference on Electrical and Computer Engineering Vol. 1, May 26-29, 1996, IEEE, Calgary, Canada, pp: 265-269.
Yao, X., 1993. A review of evolutionary artificial neural networks. Intl. J. Intell. Syst., 8: 539-567.
Direct Link | Yazdi, H.S., M. Pakdaman and H. Modaghegh, 2011. Unsupervised kernel least mean square algorithm for solving ordinary differential equations. Neurocomp., 74: 2062-2071.
CrossRef | Yentis, R. and M.E. Zaghloul, 1996. VLSI implementation of locally connected neural network for solving partial differential equations. IEEE. Trans. Circuits Syst. I. Fundam. Theor. Appl., 43: 687-690.
CrossRef | Direct Link | Zhang, J.R., J. Zhang, T.M. Lok and M.R. Lyu, 2007. A hybrid particle swarm optimization-back-propagation algorithm for feedforward neural network training. Appl. Math. Comput., 185: 1026-1037.
CrossRef | Direct Link |