Addressing climate change requires a transition to renewable energy sources. An integral part of this transition is the conversion of carbon dioxide through methanation, facilitated by the Power-to-X reactor technology. However, the implementation of this process can present significant operational hurdles, particularly in terms of control. The latter is critical to accommodate intermittent energy inputs. These challenges can be best addressed by model-based strategies. Traditional mechanistic models, while insightful, are constrained by computational limitations, highlighting the need for surrogate models. Classical machine learning techniques are indeed promising and have gained prominence, but still face some inherent obstacles. This study explores the capabilities of several (scientific) machine learning methods to develop a digital twin of a catalytic CO2 methanation reactor. Specifically, we investigate and compare Graph Neural Networks (GNNs), Operator Inference (OpInf), and Sparse Identification of Nonlinear Dynamics (SINDy) as potential surrogate modeling techniques, with the goal of combining data-driven approaches with underlying physical insights. These techniques will be compared with regard to their effectiveness in refining the dynamic operation of a CO2 methanation reactor using data-driven models derived from mechanistic frameworks. The goal is to provide interpretable, insightful mechanistic solutions that improve the efficiency and control of renewable energy conversion processes.