Unsupervised adaptive neural-fuzzy inference system for solving differential equations

There has been a growing interest in combining both neural network and fuzzy system, and as a result, neuro-fuzzy computing techniques have been evolved. ANFIS (adaptive network-based fuzzy inference system) model combined the neural network adaptive capabilities and the fuzzy logic qualitative approach. In this paper, a novel structure of unsupervised ANFIS is presented to solve differential equations. The presented solution of differential equation consists of two parts; the first part satisfies the initial/boundary condition and has no adjustable parameter whereas the second part is an ANFIS which has no effect on initial/boundary conditions and its adjustable parameters are the weights of ANFIS. The algorithm is applied to solve differential equations and the results demonstrate its accuracy and convince us to use ANFIS in solving various differential equations.