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.