Approximations of continuous functionals by neural networks with application to dynamic systems

The paper gives several strong results on neural network representation in an explicit form. Under very mild conditions a functional defined on a compact set in C[a, b] or L(p)[a, b], spaces of infinite dimensions, can be approximated arbitrarily well by a neural network with one hidden layer. The results are a significant development beyond earlier work, where theorems of approximating continuous functions defined on a finite-dimensional real space by neural networks with one hidden layer were given. All the results are shown to be applicable to the approximation of the output of dynamic systems at any particular time.