Machine Learning Kreuzer--Skarke Calabi--Yau Threefolds

TL;DR

This paper employs neural networks to analyze topological invariants of Calabi--Yau threefolds, discovering a simple, learnable expression for the Euler number from polytope data.

Contribution

It introduces a neural network approach to predict topological invariants of Calabi--Yau manifolds, revealing a straightforward formula for the Euler number based on limited polytope data.

Findings

Neural network accurately predicts Euler numbers.

Discovered a simple formula for Euler number from polytope data.

Demonstrated the effectiveness of machine learning in geometric topology.

Abstract

Using a fully connected feedforward neural network we study topological invariants of a class of Calabi--Yau manifolds constructed as hypersurfaces in toric varieties associated with reflexive polytopes from the Kreuzer--Skarke database. In particular, we find the existence of a simple expression for the Euler number that can be learned in terms of limited data extracted from the polytope and its dual.