  The prediction of spin magnitudes in binary black hole and neutron star
mergers is crucial for understanding the astrophysical processes and
gravitational wave (GW) signals emitted during these cataclysmic events. In
this paper, we present a novel Neuro-Symbolic Architecture (NSA) that combines
the power of neural networks and symbolic regression to accurately predict spin
magnitudes of black hole and neutron star mergers. Our approach utilizes GW
waveform data obtained from numerical relativity simulations in the SXS
Waveform catalog. By combining these two approaches, we leverage the strengths
of both paradigms, enabling a comprehensive and accurate prediction of spin
magnitudes. Our experiments demonstrate that the proposed architecture achieves
an impressive root-mean-squared-error (RMSE) of 0.05 and mean-squared-error
(MSE) of 0.03 for the NSA model and an RMSE of 0.12 for the symbolic regression
model alone. We train this model to handle higher-order multipole waveforms,
with a specific focus on eccentric candidates, which are known to exhibit
unique characteristics. Our results provide a robust and interpretable
framework for predicting spin magnitudes in mergers. This has implications for
understanding the astrophysical properties of black holes and deciphering the
physics underlying the GW signals.
