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

2025-02-04

AI Summary

Crystal structure prediction (CSP) faces a fundamental challenge in designing generative models that simultaneously respect crystallographic symmetry, periodicity, and physical consistency. Method: We propose the first energy-based generative framework that jointly enforces space-group invariance and atomic displacement continuity. Our approach integrates group-equivariant representation learning to rigorously preserve symmetry, incorporates periodic boundary constraints and continuous latent-space modeling to ensure geometric and energetic differentiability under translations, rotations, and infinitesimal perturbations. Contribution/Results: Evaluated on standard CSP benchmarks, our method achieves significant improvements: +23.6% space-group matching rate (symmetry fidelity), 41.2% reduction in gradient error (energy smoothness), and invalid structure rate reduced to <0.8% (physical plausibility). This establishes a new paradigm for differentiable, interpretable, and deployable crystal generation.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Generative model for crystal structure prediction
• Handles symmetry and periodicity in crystals
• Ensures invariance and continuity in predictions

Innovation

• ContinuousSP handles crystal symmetry
• Energy-based model ensures continuity
• Generative model predicts crystal structures