Rapid Parameter Estimation for Merging Massive Black Hole Binaries Using Continuous Normalizing Flows

Aug 6, 2026

Rapid, accurate parameter estimation for merging massive black hole binaries (MBHBs) is essential for space-based gravitational wave observatories such as LISA, Taiji, and Tianqin, enabling global fitting of resolvable sources and astrophysical interpretation of signals. This work addresses high computational cost by applying continuous normalizing flows (CNFs). Linear and trig interpolation define training transport paths, while a symmetry-based parameter transformation is embedded to train on simplified data and infer on general data. Experiments on simulated data yield posteriors comparable to nested sampling, achieving complete unbiased 11-dimensional rapid inference under confusion noise.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages21

Reading Time53 min

AccessFree to download

Introduction

Space-based GW detectors and MBHB science goals

Challenges: computational cost and confusion foreground

Method direction

Continuous normalizing flows for parameter estimation

arXiv :2407 .07 125v 3 [gr-qc] 5 Dec 2024 Rapid Parameter Estimation for Merging Massive Black Hole Binaries Using Continuous Normalizing Flows Bo Liang 1 2 3 4 , Minghui Du* 1 , He Wang*4 6 , Yuxiang Xu 1 2 3 4 , Chang Liu7 , Xiaotong Wei 1 , Peng Xu 1 2 4 5 , Li-e Qiang7 , Ziren Luo 1 2 4 6 1 Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China 2 Key Laboratory of Gravitational Wave Precision Measurement of Zhejiang Province, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China 3 Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China 4 Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), University of Chinese Academy of Sciences (UCAS), Beijing 100049, China 5 Lanzhou Center of Theoretical Physics, Lanzhou University, Lanzhou 730000, China 6 International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), University of Chinese Academy of Sciences (UCAS), Beijing 100049, China 7 National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China E-mail: [hewang@ucas.ac.cn](hewang@ucas.ac.cn) , [duminghui@imech.ac.cn](duminghui@imech.ac.cn) Abstract. Detecting the coalescences of massive black hole binaries (MBHBs) isone of the primary targets for space-based gravitational wave observatories such as LISA, Taiji, and Tianqin. The fast and accurate parameter estimation of merging MBHBs is of great significance for the global fitting of all resolvable sources, as well as the astrophysical interpretation of gravitational wave signals. However, such analyses usually entail significant computational costs. To address these challenges, inspired by the latest progress in generative models, we explore the application of continuous normalizing flows (CNFs) on the parameter estimation of MBHBs. Specifically, we employ linear interpolation and trig interpolation methods to construct transport paths for training CNFs. Additionally, we creatively introduce a parameter transformation method based on the symmetry in the detector’s response function. This transformation is integrated within CNFs, allowing us to train the model using a simplified dataset, and then perform parameter estimation on more general data, hence also acting as a crucial factor in improving the training speed. In conclusion, for the first time, within a comprehensive and reasonable parameter range, we have achieved a complete and unbiased 11-dimensional rapid inference for MBHBs in the presence of astrophysical confusion noise using CNFs. In the experiments based on simulated data, our model produces posterior distributions comparable to those obtained by nested sampling. 2 1. Introduction Gravitational wave (GW) astronomy has made significant progress due to the breakthroughs in ground-based detections led by the LIGO-Virgo-KAGRA network [1, 2, 3] . Scheduled in the upcoming decade, space-based detectors such as the Laser Interferometer Space Antenna (LISA) [4, 5], Taiji [6, 7, 8], and Tianqin [9, 10] aim to detect GWs in the 0 . 1 mHz - 1 Hz frequency band associated with enormous astrophysical and cosmological sources [11] . As one of the representative projects, Taiji consists of a triangle of three spacecraft (S/Cs) with a baseline separation of 3 million kilometers and aims to detect low-frequency GWs emitted by sources such as compact galactic binaries (GBs) [12], massive black hole binaries (MBHBs) [13], extreme mass ratio inspirals (EMRIs) [14], as well as the stochastic gravitational wave background of astrophysical or cosmological origins. The merger of MBHB with component masses 104 ∼ 107 M⊙ is one of the primary observation targets of space-based GW detectors, since they may shed light upon the growth and merger history of massive black holes, the dynamic behavior of curved spacetime, and the nature of gravity, etc. Due to the presence of

FAQs

Why is fast and accurate MBHB parameter estimation important for space-based detectors?

It supports global fitting of all resolvable sources and enables precise, low-latency localization (e.g., sky position) to guide electromagnetic follow-up, improving scientific interpretation of gravitational-wave data.

What approach does the paper propose to reduce computational cost?

It applies continuous normalizing flows (CNFs) to MBHB parameter estimation, using interpolation-based transport paths and an embedded symmetry-based parameter transformation to speed up training.

How does the method handle contamination from confusion foregrounds?

The experiments target parameter estimation in the presence of astrophysical confusion noise, producing posterior distributions comparable to nested sampling within a comprehensive and reasonable parameter range.

Aug 6, 2026

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