Cardiac output (CO) is a vital hemodynamic parameter that reflects the blood volume pumped by the heart per minute. A less-invasive way to estimate CO is by analyzing arterial blood pressure (ABP) waveforms. However, the relationship between CO and blood pressure is unknown. This study uses machine learning and feature engineering techniques to discover the relationship between CO and ABP. We apply the sparse identification non-linear dynamics (SINDy) algorithm to discover features. Additionally, we investigate the optimum number of cardiac cycles required for feature extraction to achieve the best performance. The proposed approach achieves clinically acceptable performance regarding radial limits of agreement (RLOA) and bias (RBias). Further, the proposed approach is validated on an external dataset. Finally, similarities to the Navier-Stokes equations are presented.