Title: Isolated pulsar population synthesis with simulation-based inference

Abstract: We combine pulsar population synthesis with simulation-based inference to constrain the magneto-rotational properties of isolated Galactic radio pulsars. We first develop a flexible framework to model neutron-star birth properties and evolution, focusing on their dynamical, rotational and magnetic characteristics. In particular, we sample initial magnetic-field strengths, $B$, and spin periods, $P$, from log-normal distributions and capture the late-time magnetic-field decay with a power law. Each log-normal 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, $a_{\rm late}$, resulting in five free parameters. We subsequently model the stars' radio emission and observational biases to mimic detections with three radio surveys, and produce a large database of synthetic $P$-$\dot{P}$ diagrams by varying our input parameters. We then follow a simulation-based inference approach that focuses on neural posterior estimation and employ this database to train deep neural networks to directly infer the posterior distributions of the five model parameters. 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 log-normal distributions, and $a_{\rm late} = -1.80^{+0.65}_{-0.61}$ for the power law at $95\%$ credible interval. Our approach represents a crucial step towards robust statistical inference for complex population-synthesis frameworks and forms the basis for future multi-wavelength analyses of Galactic pulsars.