Approximation to continuous functionals and operators using adaptive higher-order feedforward neural networks
Shuxiang Xu, Ming Zhang · 2003
The approximation capabilities of adaptive higher-order feedforward neural network (AHFNN) with neuron-adaptive activation function (NAF) to any nonlinear continuous functional and any nonlinear continuous operator are studied. Universal approximation theorems of AHFNN to continuous functionals and continuous operators are given, and learning algorithms based on the steepest descent rule are derived to tune the free parameters in NAF as well as connection weights between neurons. We apply the algorithms to approximate continuous dynamical systems.