Computational models that can predict growth and remodeling of the heart could have important clinical applications. However, the time it takes to calibrate and run current models while considering data uncertainty and variability makes them impractical for routine clinical use. This study aims to address this need by creating a computational framework to efficiently predict cardiac growth probability. We utilized a biophysics model to rapidly simulate cardiac growth following mitral valve regurgitation (MVR). Here we developed a two-tiered Bayesian History Matching approach augmented with Gaussian process emulators for efficient calibration of model parameters to align with growth outcomes within a 95% confidence interval. We first generated a synthetic data set to assess the accuracy of our framework, and the effect of changes in data uncertainty on growth predictions. We then calibrated our model to match baseline and chronic canine MVR data and used an independent data set to successfully validate the ability of our calibrated model to accurately predict cardiac growth probability. The combined biophysics and machine learning modeling framework we proposed in this study can be easily translated to predict patient-specific cardiac growth.