Transport-dominated system are known to be challenging for classical linear model order reduction (MOR) techniques. This is one of the reasons why nonlinear MOR techniques have received more and more attention in recent years. While nonlinear approaches are often able to provide low-dimensional and accurate approximations of transport-dominated phenomena, it is still challenging to construct corresponding accurate and efficient dynamic reduced-order models (ROMs). In this talk we present the combination of a recently proposed nonlinear MOR scheme based on transformed modes [1] with a Gaussian process regression approach for learning the time and parameter dependency of the ROM state, see for instance [3] for a similar approach in the context of linear MOR techniques. The presented method is non-intrusive in the sense that it is only based on snapshots of the state of the full-order model (FOM) but it does not require access to the FOM itself. Moreover, the approach does not involve time integration of a ROM and, hence, may prevent corresponding issues, such as instabilities with respect to time. We demonstrate the effectiveness of the new non-intrusive approach by means of a wildlandfire test case as in [2].