Size-Extensive Molecular Machine Learning with Global Representations

Machine learning (ML) models are increasingly used in combination with electronic structure calculations to predict molecular properties at a much lower computational cost in high-throughput settings. Such ML models require representations that encode the molecular structure, which are generally designed to respect the symmetries and invariances of the target property. However, size-extensivity is usually not guaranteed for so-called global representations. In this contribution, we show how extensivity can be built into global ML models using, e. g., the Many-Body Tensor Representation. Properties of extensive and non-extensive models for the atomization energy are systematically explored by training on small molecules and testing on small, medium and large molecules. Our results show that non-extensive models are only useful in the size-range of their training set, whereas extensive models provide reasonable predictions across large size differences. Remaining sources of error for extensive models are discussed