Machine Learning Kreuzer--Skarke Calabi--Yau Threefolds

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.

From the String Landscape to the Mathematical Landscape: a Machine-Learning Outlook

“…However, when more structures are put in, such as quiver representations [50], or tropical geometry [51], accuracies in the high 90s can once more be attained. Explorations in lattice polytopes [52,53] and knot invariants [54,55] also yield good results. Analytic Number Theory: As one might imagine, uncovering patterns in arithmetic functions, such as prime characteristic, or the likes of Mobius µ and Liouville λ, would be very hard.…”

Identifying equivalent Calabi--Yau topologies: A discrete challenge from math and physics for machine learning

“…Because there is no known algorithm for checking this equivalence, this is a natural candidate for the application of machine learning (ML) methodology. In recent years, as elaborated in some detail in the recent text [3], there has been a great deal of work on using ML methods to solve discrete problems related to Calabi-Yau geometries, with varying degrees of success [18]- [33]. On one hand, one might hope that by presenting an ML system with a variety of data of triple intersection numbers with families of equivalence known from construction it may be possible to find some approximate method for checking equivalence.…”

Brain Webs for Brane Webs

“…Neural Networks (NNs) are a primary tool within supervised ML, whose application on labelled data acts as a nonlinear function fitting to map inputs to outputs, both represented as tensors over Q using decimals. In recent years the advancement of computational power has played perfectly into the hands of these many-parameter techniques, leading to a programme of application of these tools to datasets arising in theoretical physics [18][19][20][21][22][23][24][25][26][27][28] and the relevant mathematics [29][30][31][32][33][34][35][36]. Motivated by this, we initiate the program of applying ML techniques to the classification of 5-brane webs and 5d SCFTs, concentrating on the simplest case of webs with exactly three external legs.…”