用物理信息神经网络求解 Teukolsky 方程
Solving the Teukolsky equation with physics-informed neural networks
AI总结：
本文提出用 PINNs 求解 Teukolsky 方程以计算 Kerr 黑洞准正规模，实现简单且精度通常优于1%，并验证其适用于 SNR>100 的中期引力波数据分析。
摘要：
我们使用物理信息神经网络（PINNs），通过 Teukolsky 方程计算 Kerr 几何的一阶准正规模。该技术使我们无需复杂的数值技术即可提取方程的复频率和分离常数，并且几乎可以直接在 PyTorch 框架下实现。我们能够计算任意黑洞自旋和质量下的振荡频率与阻尼时间；与文献中公认值相比，其精度通常优于百分之一量级。我们发现，在信噪比（SNRs）大于100时，由 PINN 计算的准正规模与通过现有方法得到的结果无法区分，这使得前者在中期阶段可可靠地用于引力波数据分析；在此之后，LISA 或 Einstein Telescope 等第三代探测器将到来，届时可能达到 O(1000) 的信噪比。
英文摘要：
We use physics-informed neural networks (PINNs) to compute the first quasi-normal modes of the Kerr geometry via the Teukolsky equation. This technique allows us to extract the complex frequencies and separation constants of the equation without the need for sophisticated numerical techniques, and with an almost immediate implementation under the \texttt{PyTorch} framework. We are able to compute the oscillation frequencies and damping times for arbitrary black hole spins and masses, with accuracy typically below the percentual level as compared to the accepted values in the literature. We find that PINN-computed quasi-normal modes are indistinguishable from those obtained through existing methods at signal-to-noise ratios (SNRs) larger than 100, making the former reliable for gravitational-wave data analysis in the mid term, before the arrival of third-generation detectors like LISA or the Einstein Telescope, where SNRs of ${\cal O}(1000)$ might be achieved.
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