Neural networks for functional approximation and system identification.
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.
Mhaskar
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HN
Department of Mathematics, California State University, Los Angeles 90032, USA.
Hahm
N
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D000465:Algorithms; D016015:Logistic Models; D015233:Models, Statistical; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D015203:Reproducibility of Results