Cardiac disease, including atrial fibrillation (AF), is one of the biggest causes of morbidity and mortality in the world, accounting for one third of all deaths. Cardiac modelling is now a well-established field. The Convolutional Neural Network (CNN) algorithm offer a valuable way of gaining insight into the dynamic behaviors of the heart, in normal and pathological conditions. Great efforts have been put into modelling the ventricles, whilst the atria have received less focus. This research therefore concentrates on developing models of the heart ECG atria using deep learning. The research developed an experimental result on MIT-BIH dataset for modelling myocyte electrophysiology and excitation waves in 1D & 2D tissues. It includes optimizations such as adaptive stimulus protocols. As examples of application, it is used to investigate effects of a novel anion bearing current on heart atrial excitation and the effect of remodeling on atrial myocyte electrical heterogeneity. A computationally efficient CNN anatomically based model of the heart atria is constructed. The 3D-CNN model includes heterogeneous, biophysically detailed electrophysiology and conduction anisotropy. The full model activates in 121 ms in heart rhythm, in close agreement with clinical ECG data. The model is used, with the toolkit, to investigate the function effects of S140G mutation in MIT-BIH dataset which is associated with familial. The 3D-CNN model forms the core of a boundary element model of the P-wave Body Surface Potential (BSP). The CNN model incorporates representations of the heart blood masses. Generated ECGs show qualitative agreement with clinical data. Their morphology is as expected for a healthy person, with a lead duration of 103 ms. The CNN model is used to verify an existing algorithm for focal atrial tachycardia location and in providing explanation for a novel clinical phenomenon, using CNN with 99.27% accuracy. Models of the human atria and body surface potential are constructed. The models are validated against both experimental and clinical data. These models are suitable to use as the platform for further research.