We propose herein a neural network based on curved kernels constituing an anisotropic family of functions and a learning rule to automatically tune the number of needed kernels to the frequency of the data in the input space. The model has been tested on two case studies of approximation problems known to be difficult and gave good results in comparision with traditional radial basis function (RBF) netwoks. Those examples illustrate the fact that curved kernels can locally adapt themselves to match with the observation space regularity.