Neural networks for functional approximation and system identification.

H N Mhaskar; N Hahm

doi:10.1162/neco.1997.9.1.143

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Neural networks for functional approximation and system identification.

H N Mhaskar·N Hahm

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Abstract

We construct generalized translation networks to approximate uniformly a class of nonlinear, continuous functionals defined on Lp ([-1, 1]s) for integer s > or = 1, 1 < or = p < infinity, or C ([-1, 1]s). We obtain lower bounds on the possible order of approximation for such functionals in terms of any approximation process depending continuously on a given number of parameters. Our networks almost achieve this order of approximation in terms of the number of parameters (neurons) involved in the network. The training is simple and noniterative; in particular, we avoid any optimization such as that involved in the usual backpropagation.

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Algorithms Logistic Models Models, Statistical Neural Networks, Computer Neurons Nonlinear Dynamics Normal Distribution Reproducibility of Results Journal Article Research Support, U.S. Gov't, Non-P.H.S.

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H N Mhaskar, N Hahm. 1997-01-01. Neural networks for functional approximation and system identification.. https://doi.org/10.1162/neco.1997.9.1.143

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