论文标题
从全息电导率学习黑洞度量
Learning the black hole metric from holographic conductivity
论文作者
论文摘要
我们构建了一个神经网络，以基于全息图的光导率数据来学习RN-ADS黑洞度量。麦克斯韦场的线性扰动方程是根据光导率重写的，以便基于此微分方程的离散化构建神经网络。与ADS/DL（深度学习）双重性中的所有先前模型相反，度量函数的导数出现在运动方程中，我们提出了不同的有限差异方法来离散此功能。还提出了降低的电导率的概念，以避免光导率在地平线附近的差异。训练结果对截止位置的依赖性，详细研究了温度以及频率范围。这项工作为重建散装几何形状的重建提供了一个具体的示例，并通过深度学习在边界上的给定数据。
We construct a neural network to learn the RN-AdS black hole metric based on the data of optical conductivity by holography. The linear perturbative equation for the Maxwell field is rewritten in terms of the optical conductivity such that the neural network is constructed based on the discretization of this differential equation. In contrast to all previous models in AdS/DL (deep learning) duality, the derivative of the metric function appears in the equation of motion and we propose distinct finite difference methods to discretize this function. The notion of the reduced conductivity is also proposed to avoid the divergence of the optical conductivity near the horizon.The dependence of the training outcomes on the location of the cutoff, the temperature as well as the frequency range is investigated in detail. This work provides a concrete example for the reconstruction of the bulk geometry with the given data on the boundary by deep learning.
