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