Rapid Parameter Estimation for Merging Massive Black Hole Binaries Using ODE-Based Generative Models

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 both astrophysics and the global fitting of all resolvable sources. However, such analyses entail significant computational costs. To address these challenges, inspired by the latest progress in generative models, we proposed a novel artificial intelligence (AI) based parameter estimation method called Variance Preserving Flow Matching Posterior Estimation (VPFMPE). Specifically, we utilize triangular interpolation to maintain variance over time, thereby constructing a transport path for training continuous normalization flows. Compared to the simple linear interpolation method used in flow matching to construct the optimal transport path, our approach better captures continuous temporal variations, making it more suitable for the parameter estimation of MBHBs. Additionally, we creatively introduce a parameter transformation method based on the symmetry in the detector's response function. This transformation is integrated within VPFMPE, 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 ODE-based generative models. In the experiments based on simulated data, our model produces posterior distributions comparable to those obtained by nested sampling.