  The prediction of chemical properties using Machine Learning (ML) techniques
calls for a set of appropriate descriptors that accurately describe atomic and,
on a larger scale, molecular environments. A mapping of conformational
information on a space spanned by atom-centred symmetry functions (SF) has
become a standard technique for energy and force predictions using
high-dimensional neural network potentials (HDNNP). Established atom-centred
SFs, however, are limited in their flexibility, since their functional form
restricts the angular domain that can be sampled. Here, we introduce a class of
atom-centred symmetry functions based on polynomials with compact support
called polynomial symmetry functions (PSF), which enable a free choice of both,
the angular and the radial domain covered. We demonstrate that the accuracy of
PSFs is either on par or considerably better than that of conventional,
atom-centred SFs, with reductions in force prediction errors over a test set
approaching 50% for certain organic molecules. Contrary to established
atom-centred SFs, computation of PSF does not involve any exponentials, and
their intrinsic compact support supersedes use of separate cutoff functions.
Most importantly, the number of floating point operations required to compute
polynomial SFs introduced here is considerably lower than that of other SFs,
enabling their efficient implementation without the need of highly optimised
code structures or caching, with speedups with respect to other
state-of-the-art SFs reaching a factor of 4.5 to 5. This low-effort performance
benefit substantially simplifies their use in new programs and emerging
platforms such as graphical processing units (GPU). Overall, polynomial SFs
with compact support improve accuracy of both, energy and force predictions
with HDNNPs while enabling significant speedups with respect to their
well-established counterparts.
