Deep learning black hole metrics from shear viscosity

Based on AdS/CFT correspondence, we build a deep neural network to learn black hole metrics from the complex frequency-dependent shear viscosity. The network architecture provides a discretized representation of the holographic renormalization group flow of the shear viscosity and can be applied to a large class of strongly coupled field theories. Given the existence of the horizon and guided by the smoothness of spacetime, we show that Schwarzschild and Reissner-Nordstr\"om metrics can be learned accurately. Moreover, we illustrate that the generalization ability of the deep neural network can be excellent, which indicates that by using the black hole spacetime as a hidden data structure, a wide spectrum of the shear viscosity can be generated from a narrow frequency range. These results are further generalized to an Einstein-Maxwell-dilaton black hole. Our work might not only suggest a data-driven way to study holographic transports but also shed some light on holographic duality and deep learning.