Energy storage is ubiquitous in industrial processes and comes in many forms such as material, chemical, electromechanical buffers. System identification of such energy buffers demands proper estimation/prediction of their physical quantities and unknown parameters. Once these parameters are determined, the identified model can be employed to predict the industrial process dynamics, which finally assist to build efficient control for these processes. This paper proposes physics-informed neural networks-based grey-box modeling methods for the identification of energy buffers. The underlying system dynamics are enforced on the neural network structure to ensure that the identified grey-box model follows the approximate physics. We define two novel grey-box models based on simple and recurrent neural network architectures and test these models for a generic energy buffer. Performance and training time for the proposed grey-box models are compared against a black-box baseline model. Results confirm that imposing the dynamic system’s physics on the network improves the performance, and utilizing a recurrent architecture leads to a further improvement.