Size-Extensive Molecular Machine Learning with Global Descriptors

22 October 2019, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


Machine learning (ML) models are increasingly used to predict molecular prop- erties in a high-throughput setting at a much lower computational cost than con- ventional electronic structure calculations. Such ML models require descriptors that encode the molecular structure in a vector. These descriptors are generally designed to respect the symmetries and invariances of the target property. However, size- extensivity is usually not guaranteed for so-called global descriptors. In this contri- bution, we show how extensivity can be build into ML models with global descriptors such as 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 result shows that the non-extensive model is only useful in the size-range of its training set, whereas the extensive models provide reasonable predictions across large size differences. Remaining sources of error for the extensive models are discussed.


Machine learning
Kernel ridge regression
Many-body tensor representation
Atomization energy


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