Toward Efficient and Accurate EMRI Parameter Estimation: A Machine Learning-Enhanced MCMC Framework

The detection of gravitational waves from extreme-mass-ratio inspirals (EMRIs) in space-based antennas like Taiji and Laser Interferometer Space Antenna promises deep insights into strong-field gravity and black hole physics. However, the complex, highly degenerate, and nonconvex likelihood landscapes characteristic of EMRI parameter spaces pose severe challenges for conventional Markov chain Monte Carlo (MCMC) methods. Under realistic instrumental noise and broad priors, these methods demand impractical computational costs but are prone to becoming trapped in local maxima, leading to biased and unreliable parameter estimates. To address these challenges, we introduce flow-matching MCMC (FM-MCMC), a novel Bayesian framework that integrates continuous normalizing flows (CNFs) with parallel tempering MCMC (PTMCMC). By generating high-likelihood regions via CNFs and refining them through PTMCMC, FM-MCMC enables robust exploration of the nontrivial parameter spaces, achieves orders-of-magnitude improvement in computational efficiency, and, more importantly, ensures statistically unbiased inference. By enabling real-time, unbiased parameter inference, FM-MCMC could unlock the full scientific potential of EMRI observations, and would serve as a scalable pipeline for precision gravitational-wave astronomy.