Spacetime Reconstruction from Entanglement Entropy for the Vaidya-AdS Spacetime using Machine Learning

We explore the reconstruction of bulk spacetime geometry from boundary entanglement entropy in a time-dependent holographic setting. Specifically, we study the Vaidya-AdS spacetime, which models a dynamical gravitational background corresponding to the formation of a black brane from the collapse of infalling matter. This geometry provides a dual description of a nonequilibrium quantum state undergoing thermalization. Building on recent approaches that employ machine learning to infer bulk metrics from entanglement data, we generalize these methods to explicitly time-dependent scenarios. Using numerically computed entanglement entropies of boundary subregions as input, we train a neural network–based model to reconstruct the bulk metric function and its temporal evolution. Our results demonstrate that the learned geometry accurately reproduces the Vaidya-AdS spacetime and captures the dynamical features of the spacetime. This work provides a concrete step toward spacetime reconstruction in non-stationary holographic systems and opens a path for data-driven approaches to out-of-equilibrium holography.