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Molecular fingerprints, i.e. feature vectors describing atomisticneighborhood configurations, is an important abstraction and a key ingredientfor data-driven modeling of potential energy surface and interatomic force. Inthis paper, we present the Density-Encoded Canonically Aligned Fingerprint(DECAF) fingerprint algorithm, which is robust and efficient, for fittingper-atom scalar and vector quantities. The fingerprint is essentially acontinuous density field formed through the superimposition of smoothingkernels centered on the atoms. Rotational invariance of the fingerprint isachieved by aligning, for each fingerprint instance, the neighboring atoms ontoa local canonical coordinate frame computed from a kernel minisum optimizationprocedure. We show that this approach is superior over PCA-based methodsespecially when the atomistic neighborhood is sparse and/or contains symmetry.We propose that the `distance' between the density fields be measured using avolume integral of their pointwise difference. This can be efficiently computedusing optimal quadrature rules, which only require discrete sampling at a smallnumber of grid points. We also experiment on the choice of weight functions forconstructing the density fields, and characterize their performance for fittinginteratomic potentials. The applicability of the fingerprint is demonstratedthrough a set of benchmark problems.

An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields