Based on the AdS/CFT correspondence, we build up a simple
deep neural network to learn the 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 is applicable for a large class of
strongly coupled field theories. Given the existence of the horizon
and guided by the smoothness of spacetimes, we show that the
Schwarzschild and Reissner-Nordstrom metrics can be learned
accurately. Moreover, we illustrate that the generalization ability of
the deep neural network can be excellent, which indicates that 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.
Our work might not only suggest a data-driven way to study holographic
transports, but also shed new light on the emergence mechanism of
black hole spacetimes from field theories.
BJ link: https://bluejeans.com/871723105