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Neural Computing and Applications

Erschienen in:

01.07.2014 | Original Article

Constructing Runge–Kutta methods with the use of artificial neural networks

verfasst von: Angelos A. Anastassi

Erschienen in: Neural Computing and Applications | Ausgabe 1/2014

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Abstract

A methodology that can generate the optimal coefficients of a numerical method with the use of an artificial neural network is presented in this work. The network can be designed to produce a finite difference algorithm that solves a specific system of ordinary differential equations numerically. The case we are examining here concerns an explicit two-stage Runge–Kutta method for the numerical solution of the two-body problem. Following the implementation of the network, the latter is trained to obtain the optimal values for the coefficients of the Runge–Kutta method. The comparison of the new method to others that are well known in the literature proves its efficiency and demonstrates the capability of the network to provide efficient algorithms for specific problems.

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Cybenko G (1989) Approximations by superpositions of sigmoidal functions. Math Control Signals Syst 2:303–314CrossRefMATHMathSciNet

Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Netw 4:251–257CrossRef

Dissanayake MWMG, Phan-Thien N (1994) Neural-network-based approximations for solving partial differential equations. Commun Numer Methods Eng 10:195–201CrossRefMATH

Meade AJ Jr, Fernandez AA (1994) The numerical solution of linear ordinary differential equations by feedforward neural networks. Math Comput Model 19:1–25CrossRefMATHMathSciNet

Meade AJ Jr, Fernandez AA (1994) Solution of nonlinear ordinary differential equations by feedforward neural networks. Math Comput Model 20:19–44CrossRefMATHMathSciNet

Puffer F, Tetzlaff R, Wolf D (1995) Learning algorithm for cellular neural networks (CNN) solving nonlinear partial differential equations. In: Conference Proceedings of the international symposium on signals, systems and electronics, pp 501–504

Lagaris IE, Likas A, Fotiadis DI (1998) Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Netw 9:987–1000CrossRef

He S, Reif K, Unbehauen RS (2000) Multilayer neural networks for solving a class of partial differential equations. Neural Netw 13:385–396CrossRef

Jianyu L, Siwei L, Yingjian Q, Yaping H (2002) Numerical solution of differential equations by radial basis function neural networks. Proc Int Jt Conf Neural Netw 1:773–777

10.

Alexandridis A, Chondrodima E, Sarimveis H (2013) Radial basis function network training using a nonsymmetric partition of the input space and particle swarm optimization. IEEE Trans Neural Netw Learn Syst 24:219–230CrossRef

11.

Ramuhalli P, Udpa L, Udpa SS (2005) Finite-element neural networks for solving differential equations. IEEE Trans Neural Netw 16:1381–1392CrossRef

12.

Tsoulos IG, Gavrilis D, Glavas E (2009) Solving differential equations with constructed neural networks. Neurocomputing 72(10–12):2385–2391CrossRef

13.

Tsitouras C (2002) Neural Networks with multidimensional transfer functions. IEEE Trans Neural Netw 13:222–228CrossRef

14.

Butcher JC (2003) Numerical methods for ordinary differential equations. Wiley, New YorkCrossRefMATH

15.

Haykin S (1999) Neural networks: a comprehensive foundation. Prentice Hall Englewood Cliffs, New JerseyMATH

16.

Widrow B, Hoff ME (1960) Adaptive switching circuits. IRE WESCON Conv Rec 4:96–104

17.

Yu CC, Liu BD (2002) A back-propagation algorithm with adaptive learning rate and momentum coefficient. Proc 2002 Int Jt Conf Neural Netw 2:1218–1223

Titel: Constructing Runge–Kutta methods with the use of artificial neural networks
verfasst von: Angelos A. Anastassi
Publikationsdatum: 01.07.2014
Verlag: Springer London
Erschienen in: Neural Computing and Applications / Ausgabe 1/2014
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-013-1476-x

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