The flow-induced vibration of bluff bodies is an important problem of many marine, civil, or mechanical engineers. In the design phase of such structures, it is vital to obtain good predictions of the fluid forces acting on the structure. Current methods rely on computational fluid dynamic simulations (CFD), with a too high computational cost to be effectively used in the design phase or for control applications. Alternative methods use heuristic mathematical models of the fluid forces, but these lack the accuracy (they often assume the system to be linear) or flexibility to be useful over a wide operating range.In this work we show that it is possible to build an accurate, flexible and low-computational-cost mathematical model using nonlinear system identification techniques. This model is data driven: it is trained over a user-defined region of interest using data obtained from experiments or simulations, or both. Here we use a Van der Pol oscillator as well as CFD simulations of an oscillating circular cylinder to generate the training data. Then a discrete-time polynomial nonlinear state-space model is fit to the data. This model relates the oscillation of the cylinder to the force that the fluid exerts on the cylinder. The model is finally validated over a wide range of oscillation frequencies and amplitudes, both inside and outside the so-called lock-in region. We show that forces simulated by the model are in good agreement with the data obtained from CFD.Although capable of qualitatively describing the characteristic behaviour of VIV, an efficient and powerful model, flexible enough to span a wide domain in parameter space with a single set of parameters has yet to be obtained. To identify such a model, system identification can be a very powerful tool. In recent years, the application of linear system identification techniques has already shown some promising results, e.g. the best linear approximation in least squares sense [8] or building an input-output relationship using delayed values of the input and the output (ARX model) [9].Nevertheless, the challenges in modelling the system at hand are substantial. Fluid-structure interactions are, for one, inherently nonlinear [10]. This is strongly pronounced by the fact that VIV is a selfexcited yet self-limited oscillation, resulting in a stable limit cycle [11]. In addition, it has been shown that the vortex shedding behaviour is hysteretic [12]. Nonlinear modelling of VIV is currently a very active research topic. In [13], the auto-regressive moving averaging (ARMA) technique is combined with the modal analysis method. A nonlinear force representation is obtained by including higher harmonic terms resulting from the fluid-structure coupling. The coefficients in the model are determined to provide a best fit to the measured time series in maximum-likelihood sense. Reasonable predictions in terms of maximum amplitude are found, although only a limited amount of validation cases were investigated. In recent work [14], local linear models are used as a surro...

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