  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.
