  We present thermodynamic and neutron scattering measurements on the quantum
spin ice candidate Nd$_2$Zr$_2$O$_7$. The parameterization of the anisotropic
exchange Hamiltonian is refined based on high-energy-resolution inelastic
neutron scattering data together with thermodynamic data using linear spin wave
theory and numerical linked cluster expansion. Magnetic phase diagrams are
calculated using classical Monte Carlo simulations with fields along
\mbox{[100]}, \mbox{[110]} and \mbox{[111]} crystallographic directions which
agree qualitatively with the experiment. Large hysteresis and irreversibility
for \mbox{[111]} is reproduced and the microscopic mechanism is revealed by
mean field calculations to be the existence of metastable states and domain
inversion. Our results shed light on the explanations of the recently observed
dynamical kagome ice in Nd$_2$Zr$_2$O$_7$ in \mbox{[111]} fields.
