Deep Neural Networks (DNN) enabled Cyber-Physical Systems (CPS) hold great promise for revolutionizing many industries, such as drones and self-driving cars. However, the current generation of DNN cannot provide analyzable behaviors and verifiable properties that are necessary for safety assurance. This critical flaw in purely data-driven DNN sometimes leads to catastrophic consequences, such as vehicle crashes linked to self-driving and driver-assistance technologies. On the other hand, physics-model-based engineering methods provide analyzable behaviors and verifiable properties, but do not match the performance of DNN systems. These considerations motivate the work in this project which aims at physics-model-based neural networks (NN) redesign, yielding HyPhy-DNN: a hybrid self-correcting physics-enhanced DNN framework. HyPhy-DNN will provide the performance of DNNs and the analyzability and verifiability of physical models, thus providing a foundation for verifiably safe self-driving cars, drones, and other CPS systems. Moreover, the HyPhy-DNN will fundamentally advance the integration of deep learning and robust control to enable safety- and time-critical CPS to safely operate with high performance in unforeseen and dynamic environments.