Accelerating stochastic gravitational wave backgrounds parameter estimation in pulsar timing arrays with flow matching

Pulsar timing arrays (PTAs) are essential tools for detecting the stochastic gravitational wave background (SGWB), but their analysis faces significant computational challenges. Traditional methods like Markov-chain Monte Carlo (MCMC) struggle with high-dimensional parameter spaces where noise parameters often dominate, while existing deep learning approaches have so far been validated on synthetic datasets or require training on the full pulsar set, incurring substantial computational and memory costs. We propose a flow-matching-based continuous normalizing flow (CNF) for efficient pulsar timing array (PTA) parameter estimation. Using ten pulsars selected according to published NANOGrav 12.5-year dropout factors and applied to the NANOGrav 15-year residuals, our method produces SGWB posteriors consistent with a reference MCMC analysis, with Jensen-Shannon divergences below 10 − 2 nat. After amortized training, posterior generation is reduced from approximately 50 hours for the reference MCMC pipeline to approximately 4 minutes for CNF sampling. The present study demonstrates that flow-matching-based CNFs can serve as an efficient posterior-sampling accelerator for reduced PTA datasets. Rather than providing new astrophysical constraints, the method is intended to complement conventional MCMC analyses and to provide a scalable route toward faster inference in future PTA applications.