Neural networks for interpolation of functionals on a Hilbert space

A lot of results about the interpolation by neural networks are studied on an Euclidean space Rⁿ. However, there are plenty of concrete problems happening on a Hilbert space. This paper establishes a Hilbert feed-forward neural network and deals with the interpolation of this network by a bounded nonlinear function with a limit at one infinity. The proof of our result is constructive and thus we gives a method to directly find the weights and biases of above networks as opposed to iterative training algorithms in the literature.