Unlocking New Paths for Efficient Analysis of Gravitational Waves from Extreme-Mass-Ratio Inspirals with Machine Learning

Extreme-mass-ratio inspiral (EMRI) signals pose significant challenges to gravitational wave (GW) data analysis, mainly owing to their highly complex waveforms and high-dimensional parameter space. Given their extended timescales of months to years and low signal-to-noise ratios, detecting and analyzing EMRIs with confidence generally relies on long-term observations. Besides the length of data, parameter estimation is particularly challenging due to non-local parameter degeneracies, arising from multiple local maxima, as well as flat regions and ridges inherent in the likelihood function. These factors lead to exceptionally high time complexity for parameter analysis based on traditional matched filtering and random sampling methods. To address these challenges, the present study explores a machine learning approach to Bayesian posterior estimation of EMRI signals, leveraging the recently developed flow matching technique based on ordinary differential equation (ODE) neural networks. To our knowledge, this is also the first instance of applying continuous normalizing flows (CNFs) to EMRI analysis. Our approach demonstrates an increase in computational efficiency by several orders of magnitude, compared to the traditional Markov Chain Monte Carlo (MCMC) methods, while preserving the unbiasedness of results. However, we note that the posterior distributions generated by FMPE may exhibit broader uncertainty ranges than those obtained through full Bayesian sampling, requiring subsequent refinement via methods such as MCMC. Notably, when searching from large priors, our model rapidly approaches the true values while MCMC struggles to converge to the global maximum. Our findings highlight that machine learning has the potential to efficiently handle the vast EMRI parameter space of up to seventeen dimensions, offering new perspectives for the advancement of space-based GW detection and GW astronomy.