Rapid Parameter Estimation for Extreme Mass Ratio Inspirals Using Machine Learning

TL;DR

This work shows that machine learning technology has the potential to efficiently handle the vast parameter space, involving up to seventeen parameters, associated with EMRI signals, and is the first instance of applying machine learning, specifically the Continuous Normalizing Flows (CNFs), to EMRI signal analysis.

Abstract

Extreme-mass-ratio inspiral (EMRI) signals pose significant challenges in gravitational wave (GW) astronomy owing to their low-frequency nature and highly complex waveforms, which occupy a high-dimensional parameter space with numerous variables. Given their extended inspiral timescales and low signal-to-noise ratios, EMRI signals warrant prolonged observation periods. Parameter estimation becomes 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 while employing traditional matched filtering and random sampling methods. To address these challenges, the present study applies machine learning to Bayesian posterior estimation of EMRI signals, leveraging the recently developed flow matching technique based on ODE neural networks. Our approach demonstrates computational efficiency several orders of magnitude faster than the traditional Markov Chain Monte Carlo (MCMC) methods, while preserving the unbiasedness of parameter estimation. We show that machine learning technology has the potential to efficiently handle the vast parameter space, involving up to seventeen parameters, associated with EMRI signals. Furthermore, to our knowledge, this is the first instance of applying machine learning, specifically the Continuous Normalizing Flows (CNFs), to EMRI signal analysis. Our findings highlight the promising potential of machine learning in EMRI waveform analysis, offering new perspectives for the advancement of space-based GW detection and GW astronomy.

Figures (5)

• Figure 1: Real-time GW Inference for EMRI Research: An Overview of the Framework Diagram. The left side of the diagram shows the EMRI signal dataset generated based on simulations, detailing the steps of data generation and preprocessing. The right side of the diagram displays the workflow of the machine learning model methods we employ. In sections \ref{['framework']}, we provide a detailed exposition of this framework.
• Figure 2: P-P plot for a set of 1000 injections, as analyzed by our machine learning model. We calculate the true percentile from the marginalised posterior and plot the CDF.
• Figure 3: The figure displays the posterior distribution for an EMRI, which was obtained by setting the starting points of the MCMC method close to the true parameter values. The analyzed EMRI signal has a signal-to-noise ratio (SNR) of approximately 67 and is based on two years of observational data. In the figure, the blue line represents the posterior probability distribution of the EMRI parameters, while the black line indicates the true parameter values.
• Figure 4: The left side of the figure displays for an EMRI. The starting points for the MCMC were obtained by random sampling from the prior distribution. The analyzed EMRI signal has a SNR of approximately 67 and is based on two years of observational data. In the figure, the blue line represents the posterior probability distribution of the EMRI parameters, while the black line indicates the true parameter values. The plot in the right shows the MCMC chains converging. The right side of the figure displays the convergence of the MCMC chain.
• Figure 5: The figure displays the posterior distribution for an EMRI. The analyzed EMRI signal has a SNR of approximately 67 and is based on two years of observational data. In the figure, the blue line represents the posterior probability distribution of the EMRI parameters, while the black line indicates the true parameter values.