Sleep has traditionally been manually categorised into discrete sleep stages, which is subjective and time-consuming. Recently, an objective method for analysing sleep, BrainTrak, which computes sleep trajectories from EEG recordings has been proposed. However, this method is very computationally intensive and not feasible for large scale sleep datasets. In this paper, we propose to learn a surrogate model to rapidly estimate the sleep trajectory. Specifically, we propose a neural network based approach to learn individual and ensemble surrogate models. The results showed that the surrogate models were highly accurate and significantly faster in computing the sleep trajectories - they can compute a whole night EEG trajectory in seconds, compared to BrainTrak which requires >1 week. To further demonstrate the effectiveness of the surrogate models, we used the trained surrogate models to distinguish between insomnia disorder and healthy people, with a voting classification ensemble, achieving AUC of 0.94 and accuracy of 89.2%. Another important advantage of our approach is that the use of surrogate models and sleep trajectories allows the combination of multiple EEG datasets, despite the differences in their collection, which opens new opportunities for large scale studies and analysis.