Invasive cardiac catheterisation is a precursor to ablation therapy for ventricular tachycardia. Invasive cardiac diagnostics are fraught with risks. Decades of research has been conducted on the inverse problem of electrocardiography, which can be used to reconstruct Heart Surface Potentials (HSPs) from Body Surface Potentials (BSPs), for non-invasive cardiac diagnostics. State of the art solutions to the inverse problem are unsatisfactory, since the inverse problem is known to be ill-posed. In this paper we propose a novel approach to reconstructing HSPs from BSPs using a Time-Delay Artificial Neural Network (TDANN). We first design the TDANN architecture, and then develop an iterative search space algorithm to find the parameters of the TDANN, which results in the best overall HSP prediction. We use recorded BSPs and HSPs from individuals suffering from serious cardiac conditions to validate our TDANN. The results are encouraging, in that the predicted and recorded HSPs have an average correlation coefficient of 0.7 under diseased conditions.