Machine Learning Kreuzer--Skarke Calabi--Yau Threefolds
This work addresses a specific problem in mathematical physics and string theory by applying machine learning to computational geometry, but it is incremental as it builds on existing databases and methods.
The researchers tackled the problem of predicting topological invariants of Calabi-Yau threefolds from the Kreuzer-Skarke database using a neural network, and found a simple expression for the Euler number that can be learned from limited polytope data.
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.