  We investigate the use of invariant polynomials in the construction of
data-driven interatomic potentials for material systems. The "atomic
body-ordered permutation-invariant polynomials" (aPIPs) comprise a systematic
basis and are constructed to preserve the symmetry of the potential energy
function with respect to rotations and permutations. In contrast to kernel
based and artificial neural network models, the explicit decomposition of the
total energy as a sum of atomic body-ordered terms allows to keep the
dimensionality of the fit reasonably low, up to just 10 for the 5-body terms.
The explainability of the potential is aided by this decomposition, as the low
body-order components can be studied and interpreted independently. Moreover,
although polynomial basis functions are thought to extrapolate poorly, we show
that the low dimensionality combined with careful regularisation actually leads
to better transferability than the high dimensional, kernel based Gaussian
Approximation Potential.
