NECO_a_00858-Mall neco.cls June 10, 2016 19:3 Uncorrected Proof LETTER Communicated by Miltiadis Alamaniotis Hermite Functional Link Neural Network for Solving the Van der Pol–Duffing Oscillator Equation Susmita Mall susmitalmall.05@gmail.com S. Chakraverty sne_chak@yahoo.com Department of Mathematics, National Institute of Technology Rourkela, Odisha 769008, India Hermite polynomial-based functional link artificial neural network (FLANN) is proposed here to solve the Van der Pol–Duffing oscillator equation. A single-layer hermite neural network (HeNN) model is used, where a hidden layer is replaced by expansion block of input pattern using Hermite orthogonal polynomials. A feedforward neural network model with the unsupervised error backpropagation principle is used for modifying the network parameters and minimizing the computed er- ror function. The Van der Pol–Duffing and Duffing oscillator equations may not be solved exactly. Here, approximate solutions of these types of equations have been obtained by applying the HeNN model for the first time. Three mathematical example problems and two real-life appli- cation problems of Van der Pol–Duffing oscillator equation, extracting the features of early mechanical failure signal and weak signal detection problems, are solved using the proposed HeNN method. HeNN approx- imate solutions have been compared with results obtained by the well known Runge-Kutta method. Computed results are depicted in term of graphs. After training the HeNN model, we may use it as a black box to get numerical results at any arbitrary point in the domain. Thus, the proposed HeNN method is efficient. The results reveal that this method is reliable and can be applied to other nonlinear problems too. 1 Introduction The Van der Pol–Duffing oscillator equation, a classical nonlinear oscillator, is a useful mathematical model for understanding different engineering problems. This equation is widely used to model various physical prob- lems such as electrical circuit, electronics, and mechanics (Guckenheimer & Holmes, 1983). The Van der Pol oscillator equation, proposed by Dutch scientist Balthazar Van der Pol (Tsatssos, 2006), describes triode oscillations in electrical circuits. The oscillator is a classical example of a self-oscillatory system and is now considered an important model to describe a variety Neural Computation 28, 1–25 (2016) c  Massachusetts Institute of Technology doi:10.1162/NECO_a_00858