This repository provides the implementation of Flow-Matching Markov Chain Monte Carlo (FM-MCMC), a novel Bayesian framework designed for Extreme Mass-Ratio Inspiral (EMRI) gravitational wave parameter estimation. The method integrates continuous normalizing flows (CNFs) with parallel tempering MCMC (PT-MCMC), achieving both efficiency and statistical reliability.
The code accompanies our paper:
Unlocking New Paths for Science with Extreme-Mass-Ratio Inspirals: Machine Learning-Enhanced MCMC for Accurate Parameter Inversion
Bo Liang, Chang Liu, Hanlin Song, Zhenwei Lyu, Minghui Du, Peng Xu, et al.
- EMRI signals are prime sources for space-based gravitational-wave detectors (Taiji, LISA).
- Traditional MCMC methods face severe challenges:
- prohibitively high computational costs,
- highly multimodal likelihoods with many local maxima,
- sensitivity to initialization.
FM-MCMC addresses these challenges by combining:
-
Flow Matching (FMPE):
- Uses continuous normalizing flows to learn high-likelihood regions efficiently.
- Provides informed initialization to reduce the chance of trapping in local maxima.
-
Parallel Tempering MCMC (PT-MCMC):
- Performs fine-grained posterior sampling starting from FMPE proposals.
- Ensures unbiased exploration of the parameter space.
Together, FM-MCMC achieves orders-of-magnitude speed-up while maintaining accurate and unbiased posterior estimation.
- Tested on simulated EMRI signals (Taiji noise model).
-
Intrinsic parameters (
$M, \mu, a, e_0$ ) recovered within 1σ posterior intervals for bright EMRI sources ($\text{SNR} > 60$ ). - Compared with Eryn (a state-of-the-art PT-MCMC sampler):
- FM-MCMC converges faster and avoids local maxima,
- Provides statistically reliable results under realistic noise conditions.
If you use this code, please cite our paper:
@misc{liang2025estimatingorbitalparametersdirect,
title={Estimating Orbital Parameters of Direct Imaging Exoplanet Using Neural Network},
author={Bo Liang and Hanlin Song and Chang Liu and Tianyu Zhao and Yuxiang Xu and Zihao Xiao and Manjia Liang and Minghui Du and Wei-Liang Qian and Li-e Qiang and Peng Xu and Ziren Luo},
year={2025},
eprint={2510.17459},
archivePrefix={arXiv},
primaryClass={astro-ph.EP},
url={https://arxiv.org/abs/2510.17459},
}