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The prediction of chemical properties using Machine Learning (ML) techniquescalls for a set of appropriate descriptors that accurately describe atomic and,on a larger scale, molecular environments. A mapping of conformationalinformation on a space spanned by atom-centred symmetry functions (SF) hasbecome a standard technique for energy and force predictions usinghigh-dimensional neural network potentials (HDNNP). Established atom-centredSFs, however, are limited in their flexibility, since their functional formrestricts the angular domain that can be sampled. Here, we introduce a class ofatom-centred symmetry functions based on polynomials with compact supportcalled polynomial symmetry functions (PSF), which enable a free choice of both,the angular and the radial domain covered. We demonstrate that the accuracy ofPSFs is either on par or considerably better than that of conventional,atom-centred SFs, with reductions in force prediction errors over a test setapproaching 50% for certain organic molecules. Contrary to establishedatom-centred SFs, computation of PSF does not involve any exponentials, andtheir intrinsic compact support supersedes use of separate cutoff functions.Most importantly, the number of floating point operations required to computepolynomial SFs introduced here is considerably lower than that of other SFs,enabling their efficient implementation without the need of highly optimisedcode structures or caching, with speedups with respect to otherstate-of-the-art SFs reaching a factor of 4.5 to 5. This low-effort performancebenefit substantially simplifies their use in new programs and emergingplatforms such as graphical processing units (GPU). Overall, polynomial SFswith compact support improve accuracy of both, energy and force predictionswith HDNNPs while enabling significant speedups with respect to theirwell-established counterparts.

Improved Description of Atomic Environments using Low-cost Polynomial Functions with Compact Support