Physics modeling can improve patient monitoring in clinical applications such as cardiovascular flows, but is challenging due to the limited memory and compute capability available on typical edge devices. We present a novel way to train a Physics Informed Neural Network (PINN) at the edge, while using high performance computing at the cloud, without transfer of sensitive data. This is achieved by assigning the data fitting (regression) loss to the edge where data is acquired, and the physics informed (residual) loss to the cloud where computational capabilities are ample. We find that naively optimizing two separate loss functions asynchronously at separate locations sometimes results in an accuracy drop compared to joint training, which is a problem commonly faced in continual learning. Applying Elastic Weight Consolidation (EWC), a continual learning technique, to the cloud side residual loss eliminates the accuracy gap. Our analysis shows that this is due to the larger correlation between the gradient of the residual loss and the gradient of the EWC loss. Overall, this method presents a useful way for individualized physics modeling at the edge while protecting data privacy.