# Accelerating Material Property Prediction using Generically Complete Isometry Invariants

arXiv: https://arxiv.org/abs/2401.15089 · HTML: https://mlsanity.com/paper/2401.15089/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 81 references that are in the map.
- First posted on arXiv 22 Jan 2024.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Equivariance Through Parameter-Sharing](https://mlsanity.com/paper/1702.08389/) (2017)
- [Position Information in Transformers: An Overview](https://mlsanity.com/paper/2102.11090/) (2021)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [SE(3) Equivariant Graph Neural Networks with Complete Local Frames](https://mlsanity.com/paper/2110.14811/) (2021)
- [Rotation Invariant Graph Neural Networks using Spin Convolutions](https://mlsanity.com/paper/2106.09575/) (2021)
- [Efficient Approximations of Complete Interatomic Potentials for Crystal Property Prediction](https://mlsanity.com/paper/2306.10045/) (2023)
- [Crystal Twins: Self-supervised Learning for Crystalline Material Property Prediction](https://mlsanity.com/paper/2205.01893/) (2022)
- [MOFormer: Self-Supervised Transformer model for Metal-Organic Framework Property Prediction](https://mlsanity.com/paper/2210.14188/) (2022)
- [Scalable deeper graph neural networks for high-performance materials property prediction](https://mlsanity.com/paper/2109.12283/) (2021)
- [MT-CGCNN: Integrating Crystal Graph Convolutional Neural Network with Multitask Learning for Material Property Prediction](https://mlsanity.com/paper/1811.05660/) (2018)
- [Revisiting Data Augmentation for Rotational Invariance in Convolutional Neural Networks](https://mlsanity.com/paper/2310.08429/) (2023)
- [The Density Fingerprint of a Periodic Point Set](https://mlsanity.com/paper/2104.11046/) (2021)
- [Fast predictions of lattice energies by continuous isometry invariants of crystal structures](https://mlsanity.com/paper/2108.07233/) (2021)
- [Material Property Prediction using Graphs based on Generically Complete Isometry Invariants](https://mlsanity.com/paper/2212.11246/) (2022)

## Abstract (arXiv)

Periodic material or crystal property prediction using machine learning has grown popular in recent years as it provides a computationally efficient replacement for classical simulation methods. A crucial first step for any of these algorithms is the representation used for a periodic crystal. While similar objects like molecules and proteins have a finite number of atoms and their representation can be built based upon a finite point cloud interpretation, periodic crystals are unbounded in size, making their representation more challenging. In the present work, we adapt the Pointwise Distance Distribution (PDD), a continuous and generically complete isometry invariant for periodic point sets, as a representation for our learning algorithm. The PDD distinguished all (more than 660 thousand) periodic crystals in the Cambridge Structural Database as purely periodic sets of points without atomic types. We develop a transformer model with a modified self-attention mechanism that combines PDD with compositional information via a spatial encoding method. This model is tested on the crystals of the Materials Project and Jarvis-DFT databases and shown to produce accuracy on par with state-of-the-art methods while being several times faster in both training and prediction time.