Some learning methods in functional networks

This article is devoted to learning functional networks. After a short intr oduction and motivation of functional networks using a CAD problem, four st eps used in learning functional networks are described: (1) selection of th e initial topology of the network, which is derived from the physical prope rties of the problem being modeled, (2) simplification of this topology, us ing functional equations, (3) estimation of the parameters or weights, usin g feast squares and minimax methods, and (4) selection of the subset of bas ic functions lending to the best fit to the available data, using the minim um-description-length principle. Several examples are presented to illustra te the learning procedure, including the use of a separable functional netw ork to recover the missing data of the significant wave height records in t wo different locations, based on a complete record from a third location wh ere the record is complete.