Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends critically on robust benchmarks and minimal, information-rich datasets that enable meaningful model evaluation. This paper critically examines common datasets and reported metrics for a crystal structure prediction task--generating the most likely structures given the chemical composition of a material. We focus on three key issues: First, materials datasets should contain unique crystal structures; for example, we show that the widely-utilized carbon-24 dataset only contains 40%unique structures. Second, materials datasets should not be split randomly if polymorphs of many different compositions are numerous, which we find to be the case for the perov-5 and MP-20 datasets.

Crystal structures are defined by the periodic arrangement of atoms in 3D space, inherently making them equivariant to SO(3) group. A fundamental requirement for crystal property prediction is that the model's output should remain invariant to arbitrary rotational transformations of the input structure. One promising strategy to achieve this invariance is to align the given crystal structure into a canonical orientation with appropriately computed rotations, or called frames. However, existing work either only considers a global frame or solely relies on more advanced local frames based on atoms' local structure. A global frame is too coarse to capture the local structure heterogeneity of the crystal, while local frames may inadvertently disrupt crystal symmetry, limiting their expressivity. In this work, we revisit the frame design problem for crystalline materials and propose a novel approach to construct expressive Symmetry-Preserving Frames, dubbed as SPFrame, for modeling crystal structures.

Crystal structures are defined by the periodic arrangement of atoms in 3D space, inherently making them equivariant to SO(3) group. A fundamental requirement for crystal property prediction is that the model's output should remain invariant to arbitrary rotational transformations of the input structure. One promising strategy to achieve this invariance is to align the given crystal structure into a canonical orientation with appropriately computed rotations, or called frames. However, existing work either only considers a global frame or solely relies on more advanced local frames based on atoms' local structure. A global frame is too coarse to capture the local structure heterogeneity of the crystal, while local frames may inadvertently disrupt crystal symmetry, limiting their expressivity. In this work, we revisit the frame design problem for crystalline materials and propose a novel approach to construct expressive {\bf S}ymmetry Preserving Frames, dubbed as SPFrame, for modeling crystal structures.

Protein-ligand binding prediction is a fundamental problem in AI-driven drug discovery. Previous work focused on supervised learning methods for small molecules where binding affinity data is abundant, but it is hard to apply the same strategy to other ligand classes like antibodies where labelled data is limited. In this paper, we explore unsupervised approaches and reformulate binding energy prediction as a generative modeling task. Specifically, we train an energy-based model on a set of unlabelled protein-ligand complexes using SE(3) denoising score matching (DSM) and interpret its log-likelihood as binding affinity. Our key contribution is a new equivariant rotation prediction network for SE(3) DSM called Neural Euler's Rotation Equations (NERE). It predicts a rotation by modeling the force and torque between protein and ligand atoms, where the force is defined as the gradient of an energy function with respect to atom coordinates. Using two protein-ligand and antibody-antigen binding affinity prediction benchmarks, we show that NERE outperforms all unsupervised baselines (physics-based potentials and protein language models) in both cases and surpasses supervised baselines in the antibody case.

Supervised learning with deep models has tremendous potential for applications in materials science. Recently, graph neural networks have been used in this context, drawing direct inspiration from models for molecules. However, materials are typically much more structured than molecules, which is a feature that these models do not leverage. In this work, we introduce a class of models that are equivariant with respect to crystalline symmetry groups. We do this by defining a generalization of the message passing operations that can be used with more general permutation groups, or that can alternatively be seen as defining an expressive convolution operation on the crystal graph. Empirically, these models achieve competitive results with state-of-the-art on property prediction tasks.

We consider the problem of crystal materials generation using language models (LMs). A key step is to convert 3D crystal structures into 1D sequences to be processed by LMs. Prior studies used the crystallographic information framework (CIF) file stream, which fails to ensure SE(3) and periodic invariance and may not lead to unique sequence representations for a given crystal structure. Here, we propose a novel method, known as Mat2Seq, to tackle this challenge. Mat2Seq converts 3D crystal structures into 1D sequences and ensures that different mathematical descriptions of the same crystal are represented in a single unique sequence, thereby provably achieving SE(3) and periodic invariance. Experimental results show that, with language models, Mat2Seq achieves promising performance in crystal structure generation as compared with prior methods.

We consider the problem of crystal materials generation using language models (LMs).

However, some critical aspects of it, such as the relationship between superconductivity and materials' chemical/structural features, still need to be understood. Recent successes of data-driven approaches in material science strongly inspire researchers to study this relationship with them, but a corresponding dataset is still lacking.