AbstractA Wave‐Net is an artificial neural network with one hidden layer of nodes, whose basis functions are drawn from a family of orthonormal wavelets. The good localization characteristics of the basis functions, both in the input and frequency domains, allow hierarchical, multiresolution learning of input‐output maps from experimental data. Furthermore, Wave‐Nets allow explicit estimation for global and local prediction error‐bounds, and thus lend themselves to a rigorous and explicit design of the network. This article presents the mathematical framework for the development of Wave‐Nets and discusses the various aspects of their practical implementation. Computational complexity arguments prove that the training and adaptation efficiency of Wave‐Nets is at least an order of magnitude better than other networks. In addition, it presents two examples on the application of Wave‐Nets; (a) the prediction of a chaotic time‐series, representing population dynamics, and (b) the classification of experimental data for process