ABSTRACT The afterglow emission from gamma-ray bursts (GRBs) is a valuable source of information to understand the physics of these energetic explosions. The fireball model has become the standard to describe the evolution of the afterglow emission over time and frequency. Because of recent developments in the theory of afterglows and numerical simulations of relativistic outflows, we are able to model the afterglow emission with realistic dynamics and radiative processes. Although the models agree with observations remarkably well, the afterglow emission still contains additional physics, instrumental systematics, and propagation effects that make the modelling of these events challenging. In this work, we present a new approach to modelling GRB afterglows, using Gaussian processes (GPs) to take into account systematics in the afterglow data. We show that, using this new approach, it is possible to obtain more reliable estimates of the explosion and microphysical parameters of GRBs. We present fit results for five long GRBs and find a preliminary correlation between the isotropic energetics and opening angles of GRBs, which confirms the idea of a common energy reservoir for the kinetic energy of long GRBs.