Neural network fields

In this paper, a neural network field over a subset Ξ of a metric space and a corresponding stochastic learning algorithm are introduced. A neural network field is a neural network, the parameters of which are functions of other variables, being valued in Ξ. Neural network fields are mostly dedicated to the problem of approximating a parametrized function or, more generally, to the problem of approximating a function field. Typical examples of this kind of problem may be found in the context of geophysical sciences, where the observed data depends on two or three angular variables characterizing the data acquisition process. Neural network fields also offers interesting perspectives within the field of parametric nonlinear modeling techniques.