Multilayer feedforward networks are universal approximators
Neural Networks
Regularization theory and neural networks architectures
Neural Computation
The nature of statistical learning theory
The nature of statistical learning theory
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Novel determination of differential-equation solutions: universal approximation method
Journal of Computational and Applied Mathematics
Neural Networks - 2003 Special issue: Advances in neural networks research IJCNN'03
Kernel independent component analysis
The Journal of Machine Learning Research
Adaptive Modeling of Biochemical Pathways
ICTAI '03 Proceedings of the 15th IEEE International Conference on Tools with Artificial Intelligence
Modelling the dynamics of nonlinear partial differential equations using neural networks
Journal of Computational and Applied Mathematics
Unsupervised adaptive neural-fuzzy inference system for solving differential equations
Applied Soft Computing
Artificial neural network approach for solving fuzzy differential equations
Information Sciences: an International Journal
A new modeling algorithm: normalized Kernel least mean square
IIT'09 Proceedings of the 6th international conference on Innovations in information technology
Active noise control based on kernel least-mean-square algorithm
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
IEEE Transactions on Signal Processing
The Kernel Least-Mean-Square Algorithm
IEEE Transactions on Signal Processing
Artificial neural networks for solving ordinary and partial differential equations
IEEE Transactions on Neural Networks
Comparison of artificial neural network architecture in solving ordinary differential equations
Advances in Artificial Neural Systems
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In this paper a novel method is introduced based on the use of an unsupervised version of kernel least mean square (KLMS) algorithm for solving ordinary differential equations (ODEs). The algorithm is unsupervised because here no desired signal needs to be determined by user and the output of the model is generated by iterating the algorithm progressively. However, there are several new approaches in literature to solve ODEs but the new approach has more advantages such as simple implementation, fast convergence and also little error. Furthermore, it is also a KLMS with obvious characteristics. In this paper the ability of KLMS is used to estimate the answer of ODE. First a trial solution of ODE is written as a sum of two parts, the first part satisfies the initial condition and the second part is trained using the KLMS algorithm so as the trial solution solves the ODE. The accuracy of the method is illustrated by solving several problems. Also the sensitivity of the convergence is analyzed by changing the step size parameters and kernel functions. Finally, the proposed method is compared with neuro-fuzzy [21] approach.