This paper presents a novel physics-driven spatiotemporal regularization (STRE) method for high-dimensional predictive modeling. This model not only captures the physics-based interrelationship between time-varying explanatory and response variables that are distributed in the space, but also addresses the spatial and temporal regularizations to improve the prediction performance. The STRE model is implemented to predict time-varying distributions of electric potentials on the heart surface based on the electrocardiogram (ECG) data on the body surface. The model performance is evaluated and validated in both a simulated two-sphere geometry and a realistic torso-heart geometry. Experimental results show that the STRE model significantly outperforms other models widely used in current practice such as Tikhonov zero-order, Tikhonov first-order and L1 first-order methods.