论文标题
用物理信息神经网络求解Teukolsky方程
Solving the Teukolsky equation with physics-informed neural networks
论文作者
论文摘要
我们使用物理信息神经网络（PINN）通过Teukolsky方程计算Kerr几何形状的第一个准正常模式。这种技术使我们能够在不需要复杂的数值技术的情况下提取方程的复杂频率和分离常数，并且在\ texttt {pytorch}框架下几乎立即实现。我们能够计算任意黑洞和质量的振荡频率和阻尼时间，与文献中所接受的值相比，精度通常低于百分点。我们发现，通过信噪比（SNRS）获得的现有方法大于100的现有方法获得的定量模式与大于100的现有方法没有区别，这使得前期的重力 - 波数据分析是在lisa或Einstein telescope等第三代探测器到达之前的重力波数据分析，可能是$ cals of $ cals of cal of cal of。
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.
