Astrometric constraints on stochastic gravitational wave background with neural networks

Astrometric measurements provide a unique avenue for constraining the stochastic gravitational wave background (SGWB). In this work, we investigate the application of two neural network architectures, a fully connected network and a graph neural network, for analyzing astrometric data to detect the SGWB. Specifically, we generate mock Gaia astrometric measurements of the proper motions of sources and train two networks to predict the energy density of the SGWB, $Ω_\text{GW}$. We evaluate the performance of both models under varying input datasets to assess their robustness across different configurations. We also perform a direct comparison with a likelihood-based approach using Markov chain Monte Carlo (MCMC) methods, finding out that the neural-network-based approach is significantly faster, taking on the order of minutes, compared to MCMC’s order of days, while still capturing the same features in the data. Our results demonstrate that neural networks can effectively constrain the SGWB, showing promise as tools for addressing systematic uncertainties and modeling limitations that pose challenges for traditional likelihood-based methods.

💡 Research Summary

This paper investigates the use of neural networks to constrain the stochastic gravitational‑wave background (SGWB) from astrometric data, focusing on mock Gaia proper‑motion measurements. Two architectures are explored: a fully‑connected network (FCN) and a graph neural network (GNN). The authors generate synthetic quasar catalogs with 500, 2 000 and 12 000 sources, assigning realistic G‑band magnitudes (16 < G < 20) and corresponding astrometric uncertainties using the pygaia package. An SGWB signal is injected as the quadrupole component of vector spherical harmonics; the amplitude is linked to the energy‑density parameter ΩGW via ΩGW ≈ (6/5)(1/4π) P₂ H₀⁻². Each source is described by six features (right ascension, declination, proper‑motion components in α and δ, and their uncertainties), and the target label is the injected ΩGW value drawn from a uniform