# Fast predictions of lattice energies by continuous isometry invariants of crystal structures

arXiv: https://arxiv.org/abs/2108.07233 · HTML: https://mlsanity.com/paper/2108.07233/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 11 Aug 2021.

## Builds on (most cited first, 3 of 3)

- [The Density Fingerprint of a Periodic Point Set](https://mlsanity.com/paper/2104.11046/) (2021)
- [Voronoi-based similarity distances between arbitrary crystal lattices](https://mlsanity.com/paper/2002.11165/) (2020)
- [Introduction to Periodic Geometry and Topology](https://mlsanity.com/paper/2103.02749/) (2021)

## Built on by (most cited first, 4 of 4)

- [Complete and Efficient Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2403.11857/) (2024)
- [Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives](https://mlsanity.com/paper/2303.15385/) (2023)
- [Material Property Prediction using Graphs based on Generically Complete Isometry Invariants](https://mlsanity.com/paper/2212.11246/) (2022)
- [Accelerating Material Property Prediction using Generically Complete Isometry Invariants](https://mlsanity.com/paper/2401.15089/) (2024)

## Abstract (arXiv)

Crystal Structure Prediction (CSP) aims to discover solid crystalline materials by optimizing periodic arrangements of atoms, ions or molecules. CSP takes weeks of supercomputer time because of slow energy minimizations for millions of simulated crystals. The lattice energy is a key physical property, which determines thermodynamic stability of a crystal but has no simple analytic expression. Past machine learning approaches to predict the lattice energy used slow crystal descriptors depending on manually chosen parameters. The new area of Periodic Geometry offers much faster isometry invariants that are also continuous under perturbations of atoms. Our experiments on simulated crystals confirm that a small distance between the new invariants guarantees a small difference of energies. We compare several kernel methods for invariant-based predictions of energy and achieve the mean absolute error of less than 5kJ/mole or 0.05eV/atom on a dataset of 5679 crystals.