Patients who receive transcatheter aortic valve replacement are at risk for leaflet thrombosis-related complications, and can benefit from continuous, longitudinal monitoring of the prosthesis. Conventional angiography modalities are expensive, hospital-centric and either invasive or employ potentially nephrotoxic contrast agents, which preclude their routine use. Heart sounds have been long recognized to contain valuable information about individual valve function, but the skill of auscultation is in decline due to its heavy reliance on the physician’s proficiency leading to poor diagnostic repeatability. This subjectivity in diagnosis can be alleviated using machine learning techniques for anomaly detection. We present a computational and data-driven proof-of-concept analysis of a novel, auscultation-based technique for monitoring aortic valve, which is practical, non-invasive, and non-toxic. However, the underlying mechanisms leading to physiological and pathological heart sounds are not well-understood, which hinders development of such a technique. We first address this by performing direct numerical simulations of the complex interactions between turbulent blood flow in a canonical ascending aorta model and dynamic valve motion in 29 cases with healthy and stenotic valves. Using the turbulent pressure fluctuations on the aorta lumen boundary, we model the propagation of heart sounds, as elastic waves, through the patient’s thorax. The heart sound may be recorded on the epidermal surface using a stethoscope/phonocardiograph. This approach allows us to correlate instantaneous hemodynamic phenomena and valve motion with the acoustic response. From this dataset we extract “acoustic signatures” of healthy and stenotic valves based on principal components of the recorded sound. These signatures are used to train a linear discriminant classifier by maximizing correlation between recorded heart sounds and valve status. We demonstrate that this classifier is capable of accurate prospective detection of anomalous valve function and that the principal component-based signatures capture prominent audible features of heart sounds, which have been historically used by physicians for diagnosis. Further development of such technology can enable inexpensive, safe and patient-centric at-home monitoring, and can extend beyond transcatheter valves to surgical as well as native valves.