Machine Learning: The Dimension of a Polytope

Coates, Tom; Hofscheier, Johannes; Kasprzyk, Alexander M.

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.

Citation

Coates, T., Hofscheier, J., & Kasprzyk, A. M. (2023). Machine Learning: The Dimension of a Polytope. In Machine Learning in Pure Mathematics and Theoretical Physics (85-104). World Scientific. https://doi.org/10.1142/9781800613706_0003

• Online Publication Date: Jun 26, 2023
• Publication Date: Jun 21, 2023
• Deposit Date: Mar 29, 2024
• Publisher: World Scientific
• Pages: 85-104
• Book Title: Machine Learning in Pure Mathematics and Theoretical Physics
• Chapter Number: 3
• ISBN: 978-1-80061-369-0
• DOI: https://doi.org/10.1142/9781800613706_0003
• Public URL: https://nottingham-repository.worktribe.com/output/22989959
• Publisher URL: https://www.worldscientific.com/doi/10.1142/9781800613706_0003