  We harness the physics-informed neural network (PINN) approach to extend the
utility of phenomenological models for particle migration in shear flow.
Specifically, we propose to constrain the neural network training via a model
for the physics of shear-induced particle migration in suspensions. Then, we
train the PINN against experimental data from the literature, showing that this
approach provides both better fidelity to the experiments, and a novel
understanding of the relative roles of the hypothesized migration fluxes. We
first verify the PINN approach for solving the inverse problem of radial
particle migration in a non-Brownian suspension in an annular Couette flow. In
this classical case, the PINN yields the same value (as reported in the
literature) for the ratio of the two parameters of the empirical model. Next,
we apply the PINN approach to analyze experiments on particle migration in both
non-Brownian and Brownian suspensions in Poiseuille slot flow, for which a
definitive calibration of the phenomenological migration model has been
lacking. Using the PINN approach, we identify the unknown/empirical parameters
in the physical model through the inverse solver capability of PINNs.
Specifically, the values are significantly different from those for the Couette
cell, highlighting an inconsistency in the literature that uses the latter
value for Poiseuille flow. Importantly, the PINN results also show that the
inferred values of the empirical model's parameters vary with the shear
P\'eclet number and the particle bulk volume fraction of the suspension,
instead of being constant as assumed in some previous literature.
