Prediction of the Potential Energy Surface for polyatomic molecule with the Three-dimensional Special Euclidean Equivariant Transformer Network

The process of fitting potential energy surfaces using machine learning methods typically involves manually constructing feature vectors and transforming molecular graphs into the inputs of networks for the polyatomic molecule structure. In this study, we introduce a novel approach using a three-dimensional special Euclidean equivariant transformer network that can directly learn the potential energy of polyatomic molecules and represent the structure of the molecule in a universal and interpretable way. Our method accurately predicts the potential energy of polyatomic molecules, as determined by coupled cluster theory, for various molecular graphs. Moreover, our framework is interpretable about the molecular physics, as one can extract molecular equivariant positional information regarding the global invariant energy surface. To demonstrate the utility of our approach, we present a detailed description of the training process used to fit the potential energy surfaces of polyatomic molecule CH5, as well as the properties of its resulting potential energy surfaces.