Approximation with neural networks: between local and global approximation

We investigate neural network based approximation methods. These methods depend on the locality of the basis functions. After discussing local and global basis functions, we propose a multiresolution hierarchical method. The various resolutions are stored at various levels in a tree. At the root of the tree, a global approximation is kept; the leafs store the learning samples themselves. Intermediate nodes store intermediate representations. In order to find an optimal partitioning of the input space, self-organising maps (SOM´s) are used. The proposed method has implementational problems reminiscent of those encountered in many-particle simulations. We will investigate the parallel implementation of this method, using parallel hierarchical methods for many-particle simulations as a starting point.