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

TL;DR

This paper introduces a novel application of continuous normalizing flows for rapid, unbiased 11-dimensional parameter estimation of merging massive black hole binaries, significantly reducing computational costs while maintaining accuracy.

Contribution

It presents a new method integrating parameter transformations and interpolation techniques within CNFs, enabling fast and unbiased inference in complex gravitational wave data analysis.

Findings

Achieved complete 11-dimensional inference within a reasonable parameter range.

Produced posterior distributions comparable to nested sampling methods.

Enhanced training speed through parameter transformation and simplified datasets.

Abstract

Detecting the coalescences of massive black hole binaries (MBHBs) is one 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.