Performance Verification of a Fuzzy Wavelet Neural Network in the First Order Partial Derivative Approximation of Nonlinear Functions

Approximation of the first order partial derivative of a function modeled from a set of discrete data is the requirement of several applications. However, using a direct method for calculating the partial derivative from a set of discrete points is preferred rather differentiating the function which is obtained by modeling the discrete dataset. In this paper, the first order partial derivative of a fuzzy wavelet neural network structure is calculated to act as a direct differentiator. The structure of the network is described and its parameters are tuned by an adaptive gradient-based back propagation learning algorithm. It is shown that the proposed model outperforms the adaptive neuro-fuzzy inference-based and feed forward neural network-based differentiators in approximating the first order partial derivatives of multi-variable nonlinear functions.