Neural-Network Solution of Einstein Equations for Gravity Compactifications
Represents the metric of a warped gravity compactification with a neural network and trains it by minimizing the residual of the Einstein equations, turning the construction of vacua into an optimization problem. Demonstrated by building negatively curved Einstein metrics on three-manifolds obtained by Dehn-filling the cusps of hyperbolic manifolds, as a route toward higher-dimensional Einstein metrics and de Sitter compactifications of M-theory.
2501.00093
Constructing the landscape of vacua of higher-dimensional theories of gravity by directly solving the low-energy (semi-)classical equations of motion is notoriously difficult. In this work, we invest…