Rapid advancements in machine learning (ML) are transforming materials science by significantly speeding up material property calculations. However, the proliferation of ML approaches has made it challenging for scientists to keep up with the most promising techniques. This paper presents an empirical study on Geometric Graph Neural Networks for 3D atomic systems, focusing on the impact of different (1) canonicalization methods, (2) graph creation strategies, and (3) auxiliary tasks, on performance, scalability and symmetry enforcement. Our findings and insights aim to guide researchers in selecting optimal modeling components for molecular modeling tasks.

Accelerating material discovery holds the potential to greatly help mitigate the climate crisis. Discovering new solid-state materials such as electrocatalysts, super-ionic conductors or photovoltaic materials can have a crucial impact, for instance, in improving the efficiency of renewable energy production and storage. In this paper, we introduce Crystal-GFN, a generative model of crystal structures that sequentially samples structural properties of crystalline materials, namely the space group, composition and lattice parameters. This domain-inspired approach enables the flexible incorporation of physical and structural hard constraints, as well as the use of any available predictive model of a desired physicochemical property as an objective function. To design stable materials, one must target the candidates with the lowest formation energy. Here, we use as objective the formation energy per atom of a crystal structure predicted by a new proxy machine learning model trained on MatBench. The results demonstrate that Crystal-GFN is able to sample highly diverse crystals with low (median -3.1 eV/atom) predicted formation energy.

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes transform according to the inherent physical symmetries of 3D atomic systems, including rotations and translations in Euclidean space, as well as node permutations. In recent years, Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. Their specificity lies in the inductive biases they leverage -- such as physical symmetries and chemical properties -- to learn informative representations of these geometric graphs. In this opinionated paper, we provide a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems. We cover fundamental background material and introduce a pedagogical taxonomy of Geometric GNN architectures: (1) invariant networks, (2) equivariant networks in Cartesian basis, (3) equivariant networks in spherical basis, and (4) unconstrained networks. Additionally, we outline key datasets and application areas and suggest future research directions. The objective of this work is to present a structured perspective on the field, making it accessible to newcomers and aiding practitioners in gaining an intuition for its mathematical abstractions.

The use of machine learning for material property prediction and discovery has traditionally centered on graph neural networks that incorporate the geometric configuration of all atoms. However, in practice not all this information may be readily available, e.g. when evaluating the potentially unknown binding of adsorbates to catalyst. In this paper, we investigate whether it is possible to predict a system's relaxed energy in the OC20 dataset while ignoring the relative position of the adsorbate with respect to the electro-catalyst. We consider SchNet, DimeNet++ and FAENet as base architectures and measure the impact of four modifications on model performance: removing edges in the input graph, pooling independent representations, not sharing the backbone weights and using an attention mechanism to propagate non-geometric relative information. We find that while removing binding site information impairs accuracy as expected, modified models are able to predict relaxed energies with remarkably decent MAE. Our work suggests future research directions in accelerated materials discovery where information on reactant configurations can be reduced or altogether omitted.

Mitigating the climate crisis requires a rapid transition towards lower-carbon energy. Catalyst materials play a crucial role in the electrochemical reactions involved in numerous industrial processes key to this transition, such as renewable energy storage and electrofuel synthesis. To reduce the energy spent on such activities, we must quickly discover more efficient catalysts to drive electrochemical reactions. Machine learning (ML) holds the potential to efficiently model materials properties from large amounts of data, accelerating electrocatalyst design. The Open Catalyst Project OC20 dataset was constructed to that end. However, ML models trained on OC20 are still neither scalable nor accurate enough for practical applications. In this paper, we propose task-specific innovations applicable to most architectures, enhancing both computational efficiency and accuracy. This includes improvements in (1) the graph creation step, (2) atom representations, (3) the energy prediction head, and (4) the force prediction head. We describe these contributions and evaluate them thoroughly on multiple architectures. Overall, our proposed PhAST improvements increase energy MAE by 4 to 42$\%$ while dividing compute time by 3 to 8$\times$ depending on the targeted task/model. PhAST also enables CPU training, leading to 40$\times$ speedups in highly parallelized settings. Python package: \url{https://phast.readthedocs.io}.

Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they enforce symmetries via the model architecture, which often reduces their expressivity, scalability and comprehensibility. In this paper, we introduce (1) a flexible framework relying on stochastic frame-averaging (SFA) to make any model E(3)-equivariant or invariant through data transformations. (2) FAENet: a simple, fast and expressive GNN, optimized for SFA, that processes geometric information without any symmetrypreserving design constraints. We prove the validity of our method theoretically and empirically demonstrate its superior accuracy and computational scalability in materials modeling on the OC20 dataset (S2EF, IS2RE) as well as common molecular modeling tasks (QM9, QM7-X). A package implementation is available at https://faenet.readthedocs.io.