  In this paper, we present a physics-informed neural network (PINN) approach
for predicting the performance of an all-vanadium redox flow battery, with its
physics constraints enforced by a two-dimensional (2D) mathematical model. The
2D model, which includes 6 governing equations and 24 boundary conditions,
provides a detailed representation of the electrochemical reactions, mass
transport and hydrodynamics occurring inside the redox flow battery. To solve
the 2D model with the PINN approach, a composite neural network is employed to
approximate species concentration and potentials; the input and output are
normalized according to prior knowledge of the battery system; the governing
equations and boundary conditions are first scaled to an order of magnitude
around 1, and then further balanced with a self-weighting method. Our numerical
results show that the PINN is able to predict cell voltage correctly, but the
prediction of potentials shows a constant-like shift. To fix the shift, the
PINN is enhanced by further constrains derived from the current collector
boundary. Finally, we show that the enhanced PINN can be even further improved
if a small number of labeled data is available.
