  Functional data analysis is a growing research field as more and more
practical applications involve functional data. In this paper, we focus on the
problem of regression and classification with functional predictors: the model
suggested combines an efficient dimension reduction procedure [functional
sliced inverse regression, first introduced by Ferr\'e & Yao (Statistics, 37,
2003, 475)], for which we give a regularized version, with the accuracy of a
neural network. Some consistency results are given and the method is
successfully confronted to real-life data.
