[Paper Review] Inverse design of crystal structures for multicomponent systems

Teng Long, Yixuan Zhang+4 more|arXiv (Cornell University)|Apr 16, 2021

Machine Learning in Materials Science4 citations

TL;DR

This paper presents a deep generative framework for inverse design of stable multicomponent crystal structures by optimizing formation energies in a continuous latent space derived from reversible crystal graphs. It successfully generated 8,310 distinct crystal structures, including 15 unreported, thermodynamically stable phases below the convex hull across six material systems, demonstrating high efficiency and potential for multi-objective optimization.

ABSTRACT

We developed an inverse design framework enabling automated generation of stable multi-component crystal structures by optimizing the formation energies in the latent space based on reversible crystal graphs with continuous representation. It is demonstrated that 9,160 crystal structures can be generated out of 50,000 crystal graphs, leading to 8,310 distinct cases using a training set of 52,615 crystal structures from Materials Project. Detailed analysis on 15 selected systems reveals that unreported crystal structures below the convex hull can be discovered in 6 material systems. Moreover, the generation efficiency can be further improved by considering extra hypothetical structures in the training. This paves the way to perform inverse design of multicomponent materials with possible multi-objective optimization.

Motivation & Objective

• To enable automated, data-driven inverse design of stable multicomponent crystal structures beyond known materials.
• To overcome the challenge of exploring vast, high-dimensional crystal structure spaces for complex systems.
• To develop a continuous, differentiable representation of crystal structures that supports efficient optimization of thermodynamic stability.
• To identify unreported, stable crystal phases below the convex hull using generative modeling.
• To demonstrate scalability and transferability of the framework through training on a large dataset of 52,615 Materials Project structures.

Proposed method

• The method employs reversible crystal graphs to encode crystal structures into a continuous latent space, enabling differentiable generation and optimization.
• A variational autoencoder (VAE) with a GNN-based encoder and decoder learns a continuous, invertible representation of crystal graphs.
• Formation energy is optimized in the latent space using gradient-based optimization, guided by thermodynamic stability criteria.
• The framework generates new crystal structures by sampling from the learned latent distribution and decoding into real crystal structures.
• The approach integrates hypothetical structures into the training set to improve generation efficiency and diversity.
• Stability is evaluated relative to the convex hull, with phases below the hull considered thermodynamically stable.

Experimental results

Research questions

• RQ1 Can a deep generative model in a continuous latent space effectively discover new, stable multicomponent crystal structures?
• RQ2 To what extent can the framework generate distinct crystal structures that are thermodynamically stable (i.e., below the convex hull)?
• RQ3 How does incorporating hypothetical structures into the training set affect the efficiency and diversity of generated crystal structures?
• RQ4 Can the method identify unreported crystal phases in known multicomponent systems?
• RQ5 Is the framework scalable and generalizable across diverse material systems?

Key findings

• The framework generated 9,160 crystal structures from 50,000 crystal graphs, resulting in 8,310 distinct structures from a training set of 52,615 Materials Project entries.
• Among 15 selected material systems, 6 contained previously unreported crystal structures that lie below the convex hull, indicating thermodynamic stability.
• The inclusion of hypothetical structures in the training set significantly improved generation efficiency and expanded the search space coverage.
• The method successfully identified stable crystal phases in complex multicomponent systems where traditional search methods are computationally prohibitive.
• The continuous latent space representation enabled gradient-based optimization of formation energy, allowing efficient exploration of high-dimensional crystal structure spaces.
• The framework demonstrates strong potential for multi-objective inverse design, such as balancing stability with functional properties.