[Paper Review] Inverse design of crystals using generalized invertible crystallographic representation

Zekun Ren, Juhwan Noh+11 more|arXiv (Cornell University)|May 15, 2020

Machine Learning in Materials Science49 references19 citations

TL;DR

This paper proposes a generalized invertible crystallographic representation that encodes real-space and reciprocal-space information to enable inverse design of inorganic crystals via a variational autoencoder (VAE). The method generates novel, non-existent crystal structures with targeted formation energies and band gaps, validated by first-principles calculations, and extends to semi-supervised design of thermoelectric materials despite sparse labels.

ABSTRACT

Deep learning has fostered many novel applications in materials informatics. However, the inverse design of inorganic crystals, $ extit{i.e.}$ generating new crystal structure with targeted properties, remains a grand challenge. An important ingredient for such generative models is an invertible representation that accesses the full periodic table. This is challenging due to limited data availability and the complexity of 3D periodic crystal structures. In this paper, we present a generalized invertible representation that encodes the crystallographic information into the descriptors in both real space and reciprocal space. Combining with a generative variational autoencoder (VAE), a wide range of crystallographic structures and chemistries with desired properties can be inverse-designed. We show that our VAE model predicts novel crystal structures that do not exist in the training and test database (Materials Project) with targeted formation energies and band gaps. We validate those predicted crystals by first-principles calculations. Finally, to design solids with practical applications, we address the sparse label problem by building a semi-supervised VAE and demonstrate its successful prediction of unique thermoelectric materials

Motivation & Objective

• To address the challenge of inverse design in inorganic crystals due to limited data and complex 3D periodic structures.
• To develop an invertible crystal representation that spans the full periodic table and captures both real-space and reciprocal-space features.
• To enable generative modeling of novel crystal structures with desired properties using a variational autoencoder (VAE).
• To overcome the sparse label problem in materials discovery by introducing a semi-supervised VAE for practical application targeting thermoelectric materials.
• To validate predicted crystal structures using first-principles calculations to ensure physical feasibility.

Proposed method

• Propose a generalized invertible crystallographic representation that encodes crystal structures in both real space (atomic positions and lattice vectors) and reciprocal space (Fourier-transformed periodicity).
• Integrate the invertible representation into a variational autoencoder (VAE) to learn a continuous, disentangled latent space for crystal generation.
• Train the VAE on the Materials Project database to learn the distribution of known inorganic crystals and enable latent space interpolation and generation.
• Use the VAE to generate novel crystal structures by sampling from the latent space with constraints on target properties such as formation energy and band gap.
• Implement a semi-supervised VAE framework that leverages limited labeled data (e.g., thermoelectric materials) to improve generation quality and property prediction.
• Validate predicted crystal structures using first-principles density functional theory (DFT) calculations to confirm stability and target properties.

Experimental results

Research questions

• RQ1 Can a generalized invertible crystal representation effectively encode both real-space and reciprocal-space information for diverse inorganic crystals?
• RQ2 Can a VAE trained on this representation generate novel, non-existent crystal structures with targeted formation energies and band gaps?
• RQ3 Can the model generalize to materials not present in the training or test databases of the Materials Project?
• RQ4 How effective is the semi-supervised VAE in discovering rare or practical materials like thermoelectric materials with limited labeled data?
• RQ5 Do the first-principles calculations confirm the stability and target properties of the predicted crystal structures?

Key findings

• The proposed invertible representation successfully encodes crystallographic information across the periodic table in both real and reciprocal spaces.
• The VAE generates novel crystal structures that do not exist in the Materials Project database, with formation energies and band gaps matching target values.
• First-principles calculations confirm the stability and desired electronic properties of the predicted crystal structures.
• The semi-supervised VAE successfully identifies unique thermoelectric materials despite sparse labeled data in the training set.
• The model demonstrates generalization beyond known materials, enabling discovery of new functional crystals with tailored properties.
• The integration of reciprocal-space encoding enhances the model’s ability to capture long-range periodicity and electronic structure features critical for property prediction.