# Polytopes and Machine Learning

@inproceedings{Bao2021PolytopesAM, title={Polytopes and Machine Learning}, author={Jiakang Bao and Yang-Hui He and Edward Hirst and Johannes Hofscheier and A. Kasprzyk and Suvajit Majumder}, year={2021} }

We introduce machine learning methodology to the study of lattice polytopes. With supervised learning techniques, we predict standard properties such as volume, dual volume, reflexivity, etc, with accuracies up to 100%. We focus on 2d polygons and 3d polytopes with Plücker coordinates as input, which out-perform the usual vertex representation. ar X iv :2 10 9. 09 60 2v 1 [ m at h. C O ] 1 5 Se p 20 21

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## References

SHOWING 1-10 OF 52 REFERENCES

Learning convex polytopes with margin

- MathematicsNeurIPS
- 2018

An improved algorithm for properly learning convex polytopes in the realizable PAC setting from data with a margin is presented and distinct generalizations of the notion of margin from hyperplanes to poly topes are identified.

Estimating Calabi-Yau hypersurface and triangulation counts with equation learners

- MathematicsJournal of High Energy Physics
- 2019

A bstractWe provide the first estimate of the number of fine, regular, star triangulations of the four-dimensional reflexive polytopes, as classified by Kreuzer and Skarke (KS). This provides an…

Machine learning of Calabi-Yau volumes

- Mathematics
- 2017

We employ machine learning techniques to investigate the volume minimum of Sasaki-Einstein base manifolds of noncompact toric Calabi-Yau three-folds. We find that the minimum volume can be approxim…

On the Classification of Reflexive Polyhedra

- Mathematics
- 1997

Abstract: Reflexive polyhedra encode the combinatorial data for mirror pairs of Calabi–Yau hypersurfaces in toric varieties. We investigate the geometrical structures of circumscribed polytopes with…

The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning

- Physics
- 2018

We present a pedagogical introduction to the recent advances in the computational geometry, physical implications, and data science of Calabi-Yau manifolds. Aimed at the beginning research student…

Convex lattice polytopes and cones with few lattice points inside

- Mathematics
- 2000

It is pretty well-known that toric Fano varieties of dimension k with terminal singularities correspond to convex lattice polytopes P in R^k of positive finite volume, such that intersection of P and…

On the maximum dual volume of a canonical Fano polytope

- Mathematics
- 2016

We give an upper bound on the volume vol(P*) of a polytope P* dual to a d-dimensional lattice polytope P with exactly one interior lattice point, in each dimension d. This bound, expressed in terms…

Classification of Reflexive Polyhedra in Three Dimensions

- Mathematics, Computer Science
- 1998

We present the last missing details of our algorithm for the classification of reflexive polyhedra in arbitrary dimensions. We also present the results of an application of this algorithm to the case…

Machine-Learning Mathematical Structures

- Computer ScienceInternational Journal of Data Science in the Mathematical Sciences
- 2022

Focusing on supervised machine-learning on labeled data from different fields ranging from geometry to representation theory, from combinatorics to number theory, a comparative study of the accuracies on different problems is presented.