Feedforward control is essential to achieving good tracking performance in positioning systems. The aim of this paper is to develop an identification strategy for inverse models of systems with nonlinear dynamics of unknown structure using input-output data, which can be used to generate feedforward signals for a-priori unknown tasks. To this end, inverse systems are regarded as noncausal nonlinear finite impulse response (NFIR) systems, and modeled as a Gaussian Process with a stationary kernel function that imposes properties such as smoothness. The approach is validated experimentally on a consumer printer with friction and shown to lead to improved tracking performance with respect to linear feedforward.