The present work focuses on the development of a new class of interatomic potential known as a “physically-informed neural network” (PINN) potential. This new potential format combines the high level of accuracy and flexibility associated with artificial neural networks (ANNs) with the transferability inherent to physically inspired analytic potential models. Currently we focus on single component silicon (Si) and germanium (Ge) as model systems, however, generally the PINN potential can be applied to any multicomponent metallic or covalent system. The work emphasizes various technical and procedural aspects associated with the PINN fitting and validation process as well as a demonstration of several applications. Additionally, the newly developed potentials are compared to existing classical and ANN potentials to demonstrate the increased accuracy and transferability of the PINN model.