Proof of hidden node number and experiments on RBF network for well log data inversion

Abstract

In the multilayer perceptron (MLP), there was a theorem about the maximum number of separable regions (M) given the number of hidden nodes (H) in the input d-dimensional space. We propose a recurrence relation to prove the theorem using the expansion of recurrence relation instead of proof by induction. We use three-layer radial basis function net (RBF) on the well log data inversion to test the number of hidden nodes determined by the theorem. The three-layer RBF has more nonlinear mapping. In the experiments, we have 31 simulated well log data. 25 well log data are used for training, and 6 are for testing. The experimental results can support the number of hidden nodes determined by the theorem.