Prediction of stochastic fields by RBFNN

A statistical description of stochastic phenomena is utilized to formulate a general modeler of physical laws having the structure of a radial basis function neural network. As a basis for the description of a phenomenon the concept of an auto-regressive field is utilized. Its evolution is represented by a non-linear mapping relation in which the generating function is modeled empirically by a non-parametric statistical estimator. The estimator represents a radial basis function neural network which learns from a set of empirical records of field transitions to predict the field outside some initially given domain. The performance of the generator is demonstrated by its prediction of a chaotic time series and examples of surfaces.