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Deep learning (DL) has become an essential tool in prognosis and healthmanagement (PHM), commonly used as a regression algorithm for the prognosis ofa system's behavior. One particular metric of interest is the remaining usefullife (RUL) estimated using monitoring sensor data. Most of these deep learningapplications treat the algorithms as black-box functions, giving little to nocontrol of the data interpretation. This becomes an issue if the models breakthe governing laws of physics or other natural sciences when no constraints areimposed. The latest research efforts have focused on applying complex DL modelsto achieve a low prediction error rather than studying how the models interpretthe behavior of the data and the system itself. In this paper, we propose anopen-box approach using a deep neural network framework to explore the physicsof degradation through partial differential equations (PDEs). The framework hasthree stages, and it aims to discover a latent variable and corresponding PDEto represent the health state of the system. Models are trained as a supervisedregression and designed to output the RUL as well as a latent variable map thatcan be used and interpreted as the system's health indicator.

Uncovering the Underlying Physics of Degrading System Behavior Through a Deep Neural Network Framework: The Case of Remaining Useful Life Prognosis