  Mathematical modeling of lithium-ion batteries (LiBs) is a primary challenge
in advanced battery management. This paper proposes two new frameworks to
integrate physics-based models with machine learning to achieve high-precision
modeling for LiBs. The frameworks are characterized by informing the machine
learning model of the state information of the physical model, enabling a deep
integration between physics and machine learning. Based on the frameworks, a
series of hybrid models are constructed, through combining an electrochemical
model and an equivalent circuit model, respectively, with a feedforward neural
network. The hybrid models are relatively parsimonious in structure and can
provide considerable voltage predictive accuracy under a broad range of
C-rates, as shown by extensive simulations and experiments. The study further
expands to conduct aging-aware hybrid modeling, leading to the design of a
hybrid model conscious of the state-of-health to make prediction. The
experiments show that the model has high voltage predictive accuracy throughout
a LiB's cycle life.
