  We present a novel one-fluid cavitation model of a specific Mie-Gr\"uneisen
equation of state(EOS), named polynomial EOS, based on an artificial neural
network. Not only the physics-informed equation but also the experimental data
are embedded into the proposed model by an optimization problem. The
physics-informed data-driven model provides the concerned pressure within the
cavitation region, where the density tends to zero when the pressure falls
below the saturated pressure. The present model is then applied to computing
the challenging compressible multi-phase flow simulation, such as nuclear and
underwater explosions. Numerical simulations show that our model in application
agrees well with the corresponding experimental data, ranging from one
dimension to three dimensions with the $h-$adaptive mesh refinement algorithm
and load balance techniques in the structured and unstructured grid.
