Monthly
288 pp. per issue
6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
2014 Impact factor:
2.21

Neural Computation

January 1, 1997, Vol. 9, No. 1, Pages 143-159
(doi: 10.1162/neco.1997.9.1.143)
© 1997 Massachusetts Institute of Technology
Neural Networks for Functional Approximation and System Identification
Article PDF (177.06 KB)
Abstract

We construct generalized translation networks to approximate uniformly a class of nonlinear, continuous functionals defined on Lp([—1, 1]s) for integer s ≥ 1, 1 ≤ p < ∞, 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.