  We combine pulsar population synthesis with simulation-based inference (SBI)
to constrain the magnetorotational properties of isolated Galactic radio
pulsars. We first develop a framework to model neutron star birth properties
and their dynamical and magnetorotational evolution. We specifically sample
initial magnetic field strengths, $B$, and spin periods, $P$, from lognormal
distributions and capture the late-time magnetic field decay with a power law.
Each lognormal is described by a mean, $\mu_{\log B}, \mu_{\log P}$, and
standard deviation, $\sigma_{\log B}, \sigma_{\log P}$, while the power law is
characterized by the index, $a_{\rm late}$. We subsequently model the stars'
radio emission and observational biases to mimic detections with three radio
surveys, and we produce a large database of synthetic $P$--$\dot{P}$ diagrams
by varying our five magnetorotational input parameters. We then follow an SBI
approach that focuses on neural posterior estimation and train deep neural
networks to infer the parameters' posterior distributions. After successfully
validating these individual neural density estimators on simulated data, we use
an ensemble of networks to infer the posterior distributions for the observed
pulsar population. We obtain $\mu_{\log B} = 13.10^{+0.08}_{-0.10}$,
$\sigma_{\log B} = 0.45^{+0.05}_{-0.05}$ and $\mu_{\log P} =
-1.00^{+0.26}_{-0.21}$, $\sigma_{\log P} = 0.38^{+0.33}_{-0.18}$ for the
lognormal distributions and $a_{\rm late} = -1.80^{+0.65}_{-0.61}$ for the
power law at the $95\%$ credible interval. We contrast our results with
previous studies and highlight uncertainties of the inferred $a_{\rm late}$
value. Our approach represents a crucial step toward robust statistical
inference for complex population synthesis frameworks and forms the basis for
future multiwavelength analyses of Galactic pulsars.
