  We use a 3D radiative non-ideal magnetohydrodynamic (MHD) simulation to
investigate the formation and evolution of a young protostellar disc from a
magnetized pre-stellar core. The simulation covers the first ${\sim}10~{\rm
kyr}$ after protostar formation, and shows a massive, weakly magnetized disc
with radius that initially grows and then saturates at ${\sim}30~{\rm au}$. The
disc is gravitationally unstable with prominent large-amplitude spiral arms. We
use our simulation results and a series of physical arguments to construct a
predictive and quantitative physical picture of Class 0/I protostellar disc
evolution from several aspects, including (i) the angular-momentum
redistribution in the disc, self-regulated by gravitational instability to make
most of the disc marginally unstable; (ii) the thermal profile of the disc,
well-approximated by a balance between radiative cooling and accretion heating;
and (iii) the magnetic-field strength and magnetic-braking rate inside the
disc, regulated by non-ideal magnetic diffusion. Using these physical insights,
we build a simple 1D semi-analytic model of disc evolution. We show that this
1D model, when coupled to a computationally inexpensive simulation for the
evolution of the surrounding pseudodisc, can be used reliably to predict disc
evolution in the Class 0/I phase. The predicted long-term evolution of disc
size, which saturates at ${\sim}30~{\rm au}$ and eventually shrinks, is
consistent with a recent observational survey of Class 0/I discs. Such
hierarchical modelling of disc evolution circumvents the computational
difficulty of tracing disc evolution through Class 0/I phase with direct,
numerically converged simulations.
