Crystal-LSBO: Automated Design of De Novo Crystals with Latent Space Bayesian Optimization

TL;DR

Crystal-LSBO is introduced, a de novo design framework for crystals specifically tailored to enhance explorability within LSBO frameworks, demonstrating its efficacy through optimization tasks focused mainly on formation energy values.

Abstract

Generative modeling of crystal structures is significantly challenged by the complexity of input data, which constrains the ability of these models to explore and discover novel crystals. This complexity often confines de novo design methodologies to merely small perturbations of known crystals and hampers the effective application of advanced optimization techniques. One such optimization technique, Latent Space Bayesian Optimization (LSBO) has demonstrated promising results in uncovering novel objects across various domains, especially when combined with Variational Autoencoders (VAEs). Recognizing LSBO's potential and the critical need for innovative crystal discovery, we introduce Crystal-LSBO, a de novo design framework for crystals specifically tailored to enhance explorability within LSBO frameworks. Crystal-LSBO employs multiple VAEs, each dedicated to a distinct aspect of crystal structure: lattice, coordinates, and chemical elements, orchestrated by an integrative model that synthesizes these components into a cohesive output. This setup not only streamlines the learning process but also produces explorable latent spaces thanks to the decreased complexity of the learning task for each model, enabling LSBO approaches to operate. Our study pioneers the use of LSBO for de novo crystal design, demonstrating its efficacy through optimization tasks focused mainly on formation energy values. Our results highlight the effectiveness of our methodology, offering a new perspective for de novo crystal discovery.

Figures (5)

• Figure 1: UMAP plots show the latent spaces for invalid and valid generation. A details the FTCP-VAE model's latent space, mostly leading to invalid generations with only a 49% validity rate. B displays the Combined-VAE's material latent space within the Crystal-LSBO framework, highlighting its ability to generate valid crystals even from sparse regions, with a high validity rate of 93%.
• Figure 2: The VAE model architecture in the Crystal-LSBO framework operates as follows: Step A categorizes input crystals into Lattice, Coordinate, and Element parts. Step B trains separate VAEs for these parts, obtaining their latent representations. Step C merges these representations into a unified latent space through the Combined-VAE.
• Figure 3: In the Crystal-LSBO framework, crystal generation unfolds as follows: First, latent variables $\hat{\bm{z}}$ are sampled from the material latent space. The Combined-VAE's decoder then produces specific latent representations for each VAE. Next, these representations are used by the Lattice, Coordinate, and Element-VAE decoders to generate the respective crystal components. The final structure is assembled from these components. During LSBO, this generation process is guided by the AF of BO.
• Figure 4: Panel A showcases the outcomes of using the Crystal-Standard-LSBO method for the LSBO task focused on designing de novo crystals with enhanced electronegativity values. The 20-dimensional latent space model emerged as optimal. Panel B focuses on the optimization of predicted formation energies, comparing the performance of Crystal-Standard-LSBO, Crystal-LCA-LSBO, CD-VAE, Random Search, FTCP-VAE Random Search, and FTCP-VAE Local Search. Crystal-LCA-LSBO significantly outperformed the others, while Crystal-Standard-LSBO also showed effective results.
• Figure 5: Examples of de novo crystals and their chemical compositions generated by Crystal-LCA-LSBO, showcasing diverse configurations.