Machine Learning the Dimension of a Polytope

TL;DR

This paper demonstrates that machine learning can accurately predict geometric properties such as dimension and volume of lattice polytopes from their Ehrhart series, providing a novel computational approach with high precision.

Contribution

It introduces machine learning methods to predict polytope properties from Ehrhart series, achieving near-perfect accuracy and offering mathematical insights into these relationships.

Findings

Almost 100% accuracy in predicting polytope dimension

High accuracy in recovering volume from Ehrhart series

Effective prediction of quasi-period of rational polytopes

Abstract

We use machine learning to predict the dimension of a lattice polytope directly from its Ehrhart series. This is highly effective, achieving almost 100% accuracy. We also use machine learning to recover the volume of a lattice polytope from its Ehrhart series, and to recover the dimension, volume, and quasi-period of a rational polytope from its Ehrhart series. In each case we achieve very high accuracy, and we propose mathematical explanations for why this should be so.