Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy

We investigate the bulk reconstruction of AdS black hole spacetime emergent from quantum entanglement within a machine learning framework. Utilizing neural ordinary differential equations alongside Monte-Carlo integration, we develop a method tailored for continuous training functions to extract the general isotropic bulk metric from entanglement entropy data. To validate our approach, we first apply our machine learning algorithm to holographic entanglement entropy data derived from the Gubser-Rocha and superconductor models, which serve as representative models of strongly coupled matters in holography. Our algorithm successfully extracts the corresponding bulk metrics from these data. Additionally, we extend our methodology to many-body systems by employing entanglement entropy data from a fermionic tight-binding chain at half filling, exemplifying critical one-dimensional systems, and derive the associated bulk metric. We find that the metrics for a tight-binding chain and the Gubser-Rocha model are similar. We speculate this similarity is due to the metallic property of these models.