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.

翻译：双黑洞及中子星并合事件中自旋幅度的预测，对于理解这些灾变性事件的天体物理过程及其所发射的引力波信号至关重要。本文提出了一种新颖的神经符号架构，该架构融合了神经网络与符号回归的双重能力，能够精确预测黑洞与中子星并合事件中的自旋幅度。我们的方法利用来自SXS波形目录中数值相对论模拟所得的引力波波形数据。通过结合这两种方法，我们充分发挥两种范式的优势，实现了对自旋幅度的全面且精确的预测。实验表明，所提出的架构在神经符号模型上实现了0.05的均方根误差与0.03的均方误差，而纯符号回归模型则达到了0.12的均方根误差。我们对该模型进行训练以处理高阶多极波形，并特别聚焦于已知具有独特特征的偏心候选体。研究结果为并合事件中自旋幅度的预测提供了鲁棒且可解释的框架，这对于理解黑洞的天体物理性质及破译引力波信号背后的物理机制具有重要意义。