Large cryogenic systems, like those installed at CERN, are complex systems relying on many diverse physical processes and phenomena that are difficult to simulate and monitor in detail. With only a limited number of properties measured and made available for monitoring and control purposes, several processes contributing to the dynamics of the systems are ignored. This lack of information can reduce the accuracy and the capability of a model to track, predict, and anticipate the behavior of the system. Accurate analytical or numerical computer modeling can be developed to simulate the non-linear dynamics of the processes but they are complex, computationally intensive, and cumbersome to test, validate, and implement with different configurations and limited measurements of the hidden properties. In this work, we present our investigation of using Graph Neural Networks (GNN) to build a model of the helium II bayonet heat exchanger operating in the LHC at CERN. We are proposing to use a hybrid machine learning approach, where the parameters of the GNN model are estimated by a combination of supervised learning algorithms trained on experimental data and bounding physics equations and parameters. The GNN model was initially trained on data from the experiments performed on the LHC prototype magnet strings and validated on data extracted during the operation of the LHC machine. We demonstrate the model’s accuracy, repeatability, and robustness in various configurations. The model is also well inspectable and explainable, providing the time evolution of all variables. We report on the results and expected applications, which include predictive control, diagnostic, and operator training.