Astrometric constraints on stochastic gravitational wave background with neural networks

TL;DR

This work investigates the application of two neural network architectures, a fully connected network and a graph neural network, for analyzing astrometric data to detect the SGWB, demonstrating that neural networks can effectively constrain the SGWB.

Abstract

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.

Figures (9)

• Figure 1: Illustrative graph representation for the different number of sources. The number of edges for each graph has been chosen to ensure that almost all points are connected. In this plot, the corresponding number of edges for each configuration is $n_{\text{ed},500}=3062$, $n_{\text{ed},2000}=12758$, $n_{\text{ed},12000}=75746$, respectively.
• Figure 2: Predictions in logarithmic scale on $\Omega_\text{GW}$ values, which were uniformly distributed in the range $[0,1]$. The left panel represents the result of FCN, while the right panel the one from GNN. The vertical line is the theoretical estimate for $\Omega_\text{GW}$ given by Eq. (\ref{['eq:theor_Omega_gw']}). The predicted values are obtained using the test set ($1600$ samples, the $20\%$ of the original dataset of $8000$ mocks).
• Figure 3: Test of trained FCN and GNN networks to new test datasets obtained by fixing $\Omega_\text{GW}$ to $0.03\,,0.3\,,1.0$ values. Each violin illustrates the aggregated distribution of predictions across 100 independent realizations for each fixed value. Results are shown for different values of $N_s$, with corresponding MSE values reported in Table \ref{['tabel:mse']}.
• Figure 4: Comparison in logarithmic scale between MCMC (orange) and FCN (blue) predictions on $\Omega_\text{GW}$ values, uniformly distributed in the range $[0,1]$. The number of test samples is $1600$ for the case $N_s=2000$.
• Figure 5: The probability distribution of deviations between the true and predicted values for $\Omega_\text{GW}$ is plotted using the results obtained from the test dataset in Fig. \ref{['fig:nn_predictions']}. The cyan curve represents the Gaussian fit to the FCN results, while the blue curve represents the Gaussian fit to the GNN results.