Surrogate deep neural networks (DNNs) can significantly speed up the engineering design process by providing a quick prediction that emulates simulated data. Many previous works have considered improving the accuracy of such models by introducing additional physics-based loss terms (physics-informed neural networks or PINNs). However, PINNs are more computationally expensive and often more difficult to tune than DNNs. We propose combining the two approaches by first training an unsupervised PINN to solve a simplified physics problem and then using its output as additional input features for the surrogate DNN. This method can potentially be more accurate than a simple DNN, while being simpler to train than a PINN on complex multiscale physics problems. Furthermore, it could be preferable in transfer learning scenarios, as the PINN, which provides the basis for the surrogate DNN's prediction, does not depend on data. We tested our approach by comparing the performance of a geometric DNN for the prediction of 2D incompressible fluid flow around airfoils with and without additional physics features (potential flow solution by a PINN). We observed a slight improvement in test prediction accuracy and a decrease in the difference between train and test accuracy.