Crystal Diffusion Variational Autoencoder for Periodic Material Generation

Abstract

Generating the periodic structure of stable materials is a long-standing challenge for the material design community. This task is difficult because stable materials only exist in a low-dimensional subspace of all possible periodic arrangements of atoms: 1) the coordinates must lie in the local energy minimum defined by quantum mechanics, and 2) global stability also requires the structure to follow the complex, yet specific bonding preferences between different atom types. Existing methods fail to incorporate these factors and often lack proper invariances. We propose a Crystal Diffusion Variational Autoencoder (CDVAE) that captures the physical inductive bias of material stability. By learning from the data distribution of stable materials, the decoder generates materials in a diffusion process that moves atomic coordinates towards a lower energy state and updates atom types to satisfy bonding preferences between neighbors. Our model also explicitly encodes interactions across periodic boundaries and respects permutation, translation, rotation, and periodic invariances. We significantly outperform past methods in three tasks: 1) reconstructing the input structure, 2) generating valid, diverse, and realistic materials, and 3) generating materials that optimize a specific property. We also provide several standard datasets and evaluation metrics for the broader machine learning community.

Physics Guided Deep Learning for Generative Design of Crystal Materials with Symmetry Constraints

“…Two baseline methods are compared and PGCGM achieves the best performance across all evaluation metrics. In particular, PGCGM significantly outperforms the two baseline models in terms of property distribution metric which is a much stronger indicator to show the reality of the generated materials [35]. In addition, we use BOWSR to optimize 2000 randomly selected methods in each method.…”

“…Another approach to represent 3D crystals is to encode 2D crystallographic representations as the combination of real space and reciprocal-space Fourier-transformed features [29]. In CDVAE [35], authors propose to generate materials in a diffusion process [15] in the decoder. The diffusion process moves atoms into positions in the lower energy space to generate stable crystals.…”

“…Despite the success of VAEs and GANs in material generation [24,35,36], current generative models all have several major drawbacks. For example, the iMatGen algorithm [24] can only focus on a specific chemical system such as vanadium oxides and only several new metastable VxOy materials were discovered out of 20,000 generated hypothetical materials.…”

SELFIES and the future of molecular string representations

“…A numerical encoding of LQG, the Systre key [85], was implemented to identify nets. More recently, the LQG implementation was employed in crystal structure generation using a VAE [86]. While the current SELFIES scheme is able to represent molecules with localized bonds robustly, to represent an LQG, several improvements are needed:…”

Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas

“…Associated implementations such as the PESNet attempt to curtail the learning process of a potential energy surface [25] and the neural canonical transformation for the computation of the electron effective mass [37]. Finally, there is work on incorporating periodic functions to neural networks and/or applying these methods to periodic data/systems [38,39] and equivariances to periodic data [40,41].…”