论文标题
使用物理信息神经网络计算准模式
Using physics-informed neural networks to compute quasinormal modes
论文作者
论文摘要
近年来，人们对神经网络的兴趣增加了，特别是关于它们近似部分微分方程的能力。在这方面，研究已经开始对所谓的物理信息神经网络（PINN）进行研究，这些神经网络（PINN）纳入了其损失功能，即他们试图近似的功能的边界条件。在本文中，我们研究了使用PINN在4维时空中获得非旋转黑洞的准正常模式（QNM）的生存能力，我们发现可以使用能够解决特征值问题的标准方法（在此处使用特征值求解器）来实现。与通过更确定的方法获得的QNM相比（即，持续的分数方法和第六阶温格策尔，克莱默，布里群方法）PINN计算具有与这些对应方相同的准确性。换句话说，我们的PINN近似值的百分比偏差低至$（ΔΩ_{_ {re}}，ΔΩ__ {_ {im}}）=（<0.01 \％，<0.01 \％）$。但是，就计算QNM所花费的时间而言，Pinn方法不足，因此得出的结论是，在考虑整体性能时，目前不建议使用该方法。
In recent years there has been an increased interest in neural networks, particularly with regard to their ability to approximate partial differential equations. In this regard, research has begun on so-called physics-informed neural networks (PINNs) which incorporate into their loss function the boundary conditions of the functions they are attempting to approximate. In this paper, we investigate the viability of obtaining the quasi-normal modes (QNMs) of non-rotating black holes in 4-dimensional space-time using PINNs, and we find that it is achievable using a standard approach that is capable of solving eigenvalue problems (dubbed the eigenvalue solver here). In comparison to the QNMs obtained via more established methods (namely, the continued fraction method and the 6th-order Wentzel, Kramer, Brillouin method) the PINN computations share the same degree of accuracy as these counterparts. In other words, our PINN approximations had percentage deviations as low as $(δω_{_{Re}}, δω_{_{Im}}) = (<0.01\%, <0.01\%)$. In terms of the time taken to compute QNMs to this accuracy, however, the PINN approach falls short, leading to our conclusion that the method is currently not to be recommended when considering overall performance.
