Generating Triangulations and Fibrations with Reinforcement Learning

TL;DR

This paper introduces a reinforcement learning approach to generate triangulations and fibrations of reflexive polytopes, enabling the search for Calabi-Yau hypersurfaces with desirable string compactification properties.

Contribution

It presents a novel RL-based method for generating triangulations and fibrations of reflexive polytopes, facilitating the exploration of Calabi-Yau manifolds with specific physical conditions.

Findings

RL can generate triangulations satisfying anomaly cancellation.

The method finds fibrations of Calabi-Yau hypersurfaces.

It enables targeted searches for string compactification features.

Abstract

We apply reinforcement learning (RL) to generate fine regular star triangulations of reflexive polytopes, that give rise to smooth Calabi-Yau (CY) hypersurfaces. We demonstrate that, by simple modifications to the data encoding and reward function, one can search for CYs that satisfy a set of desirable string compactification conditions. For instance, we show that our RL algorithm can generate triangulations together with holomorphic vector bundles that satisfy anomaly cancellation and poly-stability conditions in heterotic compactification. Furthermore, we show that our algorithm can be used to search for reflexive subpolytopes together with compatible triangulations that define fibration structures of the CYs.