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ContinuouSP: Generative Model for Crystal Structure Prediction with Invariance and Continuity

Yuji Tone, Masatoshi Hanai, Mitsuaki Kawamura, Kenjiro Taura, Toyotaro Suzumura

TL;DR

A new model is proposed, called ContinuouSP, which effectively handles symmetry and periodicity in crystals, and is constructed based on the energy-based model.

Abstract

The discovery of new materials using crystal structure prediction (CSP) based on generative machine learning models has become a significant research topic in recent years. In this paper, we study invariance and continuity in the generative machine learning for CSP. We propose a new model, called ContinuouSP, which effectively handles symmetry and periodicity in crystals. We clearly formulate the invariance and the continuity, and construct a model based on the energy-based model. Our preliminary evaluation demonstrates the effectiveness of this model with the CSP task.

ContinuouSP: Generative Model for Crystal Structure Prediction with Invariance and Continuity

TL;DR

A new model is proposed, called ContinuouSP, which effectively handles symmetry and periodicity in crystals, and is constructed based on the energy-based model.

Abstract

The discovery of new materials using crystal structure prediction (CSP) based on generative machine learning models has become a significant research topic in recent years. In this paper, we study invariance and continuity in the generative machine learning for CSP. We propose a new model, called ContinuouSP, which effectively handles symmetry and periodicity in crystals. We clearly formulate the invariance and the continuity, and construct a model based on the energy-based model. Our preliminary evaluation demonstrates the effectiveness of this model with the CSP task.

Paper Structure

This paper contains 35 sections, 11 theorems, 20 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Crystal Property Prediction
  4. CSP and Crystal Generation
  5. Continuity of Machine Learning Models
  6. Energy-Based Models
  7. Preliminaries
  8. Solid Materials
  9. Crystals
  10. Crystal Graph Convolutional Neural Networks
  11. Energy-Based Models
  12. Proposed Method
  13. Experiment
  14. Experimental Setup
  15. Crystal Structure Prediction
  16. ...and 20 more sections

Key Result

Theorem 1

$\mathrm{CGCNN}_\theta$ is strongly re-description invariant. Also, $\mathrm{CGCNN}_\theta \circ \mathrm{PtoS}^{-1}$ is invariant to translation and rotation.

Figures (2)

  • Figure 1: Diagram illustrating the training workflow of ContinuouSP: For each periodic unit of the crystal included in the training data points, the species vector is $\mathrm{Reduce}$-d to the composition, then $\mathrm{Expand}$-ed using a geometric distribution to create a new species vector. This vector is used to condition the sampling performed via MCMC. The resulting new crystal and the original crystal are compared by calculating the energy difference, which is used as a pseudo-loss.
  • Figure 2: The results of the displacement vs. energy experiment: For crystals with stable structures, an atom is selected from the periodic unit, and Gaussian noise is added to its coordinates. The diagram shows the relationship between the displacement and the energy output by the model. From top to bottom, the results correspond to crystals picked from the Perov-5, MP-20, and MPTS-52 datasets, respectively. Note that the format of IDs representing crystals varies across datasets. The relationship between displacement and energy is divided into two types: those where energy monotonically increases with displacement and those where both increases and decreases are observed.

Theorems & Definitions (44)

  • Definition 1: Solid Materials
  • Definition 2: Translation Invariance on Solid Materials
  • Definition 3: Rotation Invariance on Solid Materials
  • Definition 4: Continuity on Solid Materials
  • Definition 5: Periodic Units
  • Definition 6: Periodic Units to Solid Materials
  • Definition 7: Strong Re-description Invariance
  • Definition 8: Weak Re-description Invariance
  • Definition 9: Graph Construction in CGCNN
  • Definition 10: Graph Convolution in CGCNN
  • ...and 34 more