Accelerating Stochastic Gravitational Wave Backgrounds Parameter Estimation in Pulsar Timing Arrays with Flow Matching

Abstract

\Acp{PTA} are essential tools for detecting the \ac{SGWB}, but their analysis faces significant computational challenges. Traditional methods like \ac{MCMC} struggle with high-dimensional parameter spaces where noise parameters often dominate, % while existing deep learning approaches fail to model the \ac{HD} correlation or are validated only on synthetic datasets. 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 \ac{CNF} for efficient \ac{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 \ac{SGWB} posteriors consistent with a reference \ac{MCMC} analysis, with Jensen-Shannon divergences below \(10^{-2}\) nat. After amortized training, posterior generation is reduced from approximately 50 hours for the reference \ac{MCMC} pipeline to approximately 4 minutes for \ac{CNF} sampling. The present study demonstrates that flow-matching-based \acp{CNF} can serve as an efficient posterior-sampling accelerator for reduced \ac{PTA} datasets. Rather than providing new astrophysical constraints, the method is intended to complement conventional \ac{MCMC} analyses and to provide a scalable route toward faster inference in future \ac{PTA} applications.