P. Berglund

G. Butbaia

Y. He

E. Heyes

E. Hirst

V. Jejjala

Machine learning generates desirable triangulations of geometric objects that are required for Calabi-Yau compactification in string theory.

Reinforcement learning produces fine, regular, star triangulations of reflexive polytopes in four dimensions that result in smooth Calabi-Yau threefolds. The approach can be used to search for threefolds satisfying desirable string theory compactification conditions. More refined properties such as stable vector bundles on the threefolds, as well as fibration structure can be generated by modifying the cost function.

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.

Triangulating polytopes

Generating triangulations and fibrations with reinforcement learning