Computational models give us insights into physiological processes and help to develop novel treatment strategies in the biomedical field. However, their complexity and non-linearity make them computationally expensive and challenging to analyse. Reduced or linearised representations of these models can help overcome these issues. A potential application of such models addresses the design of physiological control algorithms for vagus nerve stimulation (VNS). Here models will be essential to control stimulation and regulate the cardiovascular system function improving clinical outcomes. In this thesis steps to address this problem have been investigated using a deep neural network approach to Koopman analysis (DNN-KA). DNN-KA uses deep learning to globally linearise dynamics on a low-dimensional manifold by identifying non-linear coordinates with a modified autoencoder.