Extracting the faint gravitational-wave background (GWB) signal from dominant detector noise and disentangling its astrophysical and cosmological components remain significant challenges for traditional methods like cross-correlation analysis. We propose a novel hybrid approach that combines deep learning with Bayesian inference to identify and characterize the GWB more rapidly than current techniques. Our method utilizes a custom-designed multiscale multiheaded autoencoder (MSMHAutoencoder) architecture to separate GWB signals from detector noise and, subsequently, Markov chain Monte Carlo parameter estimation to disentangle the GWB components. Using simulated data representative of the LIGO-Virgo-KAGRA network at design sensitivity, we show that our MSMHAutoencoder can detect with high confidence (log noise Bayes factor of 3) a GWB from compact binary mergers with fractional energy density ${\mathrm{\Omega }}_{\mathrm{CBC}}\approx {10}^{-9}$ at 25 Hz. In the presence of such an astrophysical GWB, we can simultaneously measure a flat cosmological component as faint as ${\mathrm{\Omega }}_{\text{cosmo}}\approx 1.3\times {10}^{-10}$ using 47.4 days of training data.

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• Gravitational wave detection
• Gravitational waves
• Bayesian networks
• Convolutional neural networks
• Astrophysical & cosmological simulations
• Stochastic analysis methods