ABSTRACT
This chapter introduces various types of functional link artificial neural network (FLANN) models to handle ordinary differential equations (ODEs). FLANN models are fast-learning single-layer artificial neural network (ANN) models. The single-layer FLANN method is introduced by Pao and Philips. In FLANN, the hidden layer is replaced by a functional expansion block for enhancement of the input patterns using orthogonal polynomials such as Chebyshev, Legendre, Hermite, etc. The chapter explains the structure of single-layer FLANN models, and explains the formulations and gradient computations. In FLANN, the total number of network parameters is less than that of the multilayer perceptron (MLP) structure. So the technique is computationally more efficient than MLP. The chapter discusses some of the advantages of the single-layer FLANN-based model for solving differential equations. It reviews the structure of single-layer simple orthogonal polynomial–based neural network model.
