  A new framework of thermodynamic modeling is proposed by introducing the
concept of differentiable programming, where all the thermodynamic observables
including both thermochemical quantities and phase equilibria can be
differentiated with respect to the underlying model parameters, thus allowing
the models learned by gradient-based optimization. It is shown that
thermodynamic modeling and deep learning can be seamlessly integrated and
unified within this framework. A preliminary successful application is
demonstrated for the Cu-Rh system. It is expected that thermodynamic modeling
in a deep learning style can increase prediction power of models, and provide
more effective guidance for design, synthesis and optimization of
multi-component materials with complex chemistry via learning various types of
data.
