Parameter estimation for stochastic gravitational wave backgrounds with space-based detectors via sequential neural posterior estimation

With the progression of space based gravitational wave missions such as LISA, Taiji, and TianQin, extracting faint stochastic gravitational wave backgrounds from complex detector noise has emerged as a pivotal challenge in data processing. Due to the intricate observational environment, instrumental noise significantly overlaps with astrophysical and cosmological signals in the frequency domain, imposing a substantial computational burden on traditional sampling methods within high dimensional parameter spaces. In this study, we employ a Sequential Neural Posterior Estimation (SNPE) framework, utilizing Normalizing Flows to learn the mapping between simulated data and parameters. An 11 dimensional parameter analysis model is constructed, encompassing background amplitudes, spectral indices, confusion noise, and instrumental noise. The results demonstrate that the posterior distributions obtained via SNPE are consistent with the Markov Chain Monte Carlo references in both profile and location for multi source signals. Quantitative analysis using Jensen Shannon Divergence reveals that the discrepancies for most parameters remain at an extremely low level, typically below 0.04, validating the reliability of the SNPE framework for SGWB signal separation and parameter estimation. While maintaining analytical precision, this approach demonstrates significant potential for handling high dimensional complex data, offering a robust technical path for future space based gravitational wave data analysis.