Prediction of Forces and Energy Based on Rotational Invariant Spherical Representations.

Although hand-crafted descriptor-based methods have traditionally been used to construct accurate machine learning interatomic potentials, graph neural networks (GNNs), which can be trained end-to-end, have recently attracted attention due to their generality.<br/>GNNs use rotational-invariant geometric features of materials, such as interatomic distances, and bond angles, to model interactions with neighboring atoms [1]. Recently, many efforts have been made to improve the prediction accuracy of equivariant quantities such as interatomic forces by imposing not only invariance but also equivariance on the model [2].<br/>However, imposing equivariance imposes restrictions on the operations in the model and prevents the use of nonlinear transformations, which are particularly important for improving expressiveness. In addition, to express equivariance, higher-order tensor features may be required, and equivariant operations are expensive in terms of computational cost.<br/>In response to these problems, previous studies have taken steps to loosen the restriction on nonlinearity by sampling points on a sphere or to lower the dimensionality of features by approximating equivariant operations [3], and efforts to develop equivariant models with excellent expressive power and computational cost [4].<br/>In this study, we developed a GNN architecture for equivariant prediction with excellent expressiveness and computational cost by using a different method from these studies. We improved the efficiency by converting the rotational equivariant inter-atomic directional information into a rotational invariant representation, eliminating the limitations of nonlinearity, and incorporating efficient geometric message passing [5].<br/>First, to make the directional information between atoms invariant, the coordinates of the neighborhood atoms were transformed using an orthonormal basis defined between two different neighborhood atoms and the central atom. This allows us to obtain directional information between atoms that is invariant to global rotations.<br/>Next, the invariants created by the transformation and the geometric message passing proposed in previous studies were used to update the graph embedding vectors. Note that since only invariant features are used, the embedding itself is an invariant and there are no nonlinearity restrictions when updating it. The geometric message passing proposed in the previous study involves a very expensive operation, as it requires the calculation of the dihedral angles for a quartet of atoms in the material. In this study, the coordinate transformation allows us to efficiently consider higher-order geometric features, thus constituting geometrical message passing with excellent computational cost.<br/>Finally, the predictions were made by extending the embedding vector, which is an invariant, to an equivariant in a manner similar to previous studies. Previous studies have already proven the extension from invariants to equivariants to be general [5].<br/>This presentation will provide an overview of the developed model and the results of validating its accuracy and throughput on several data sets and comparing it to existing models.<br/>[1] C. Chen and S. P. Ong, Nature Computational Science. 2, 718–728 (2022).<br/>[2] K. T. Schütt et al., arXiv 2102.03150 (2021).<br/>[3] C. Lawrence Zitnick et al., arXiv 2206.14331 (2022).<br/>[4] S. Passaro and C. Lawrence Zitnick, arXiv 2302.0365 (2023).<br/>[5] J. Gasteiger et al., arXiv 2106.08903 (2021).