ABSTRACT The detailed modelling of stellar oscillations is a powerful approach to characterizing stars. However, poor treatment of systematics in theoretical models leads to misinterpretations of stars. Here, we propose a more principled statistical treatment for the systematics to be applied to fitting individual mode frequencies with a typical stellar model grid. We introduce a correlated noise model based on a Gaussian process (GP) kernel to describe the systematics given that mode frequency systematics are expected to be highly correlated. We show that tuning the GP kernel can reproduce general features of frequency variations for changing model input physics and fundamental parameters. Fits with the correlated noise model better recover stellar parameters than traditional methods that either ignore the systematics or treat them as uncorrelated noise.