While phonon dispersion curves only depend on 2 nd order force constants, the calculation of Grüneisen parameters requires an accurate description of quasi-harmonic force constants (the first derivatives of frequencies with respect to volume). Therefore, the Grüneisen parameters provide a more stringent test for the accuracy of the GAP models. Our results show that the MLIPs developed in this study are quite successful at predicting quasi-harmonic interactions, with the exception of silicene, where there is an overestimation at low frequencies. In addition, based on the Grüneisen approximation of thermal expansion theory, the generated GAP models yield accurate results for the thermal expansion properties of these materials.