Title: An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields,
Abstract: Molecular fingerprints, i.e. feature vectors describing atomistic
neighborhood configurations, is an important abstraction and a key ingredient
for data-driven modeling of potential energy surface and interatomic force. In
this paper, we present the Density-Encoded Canonically Aligned Fingerprint
(DECAF) fingerprint algorithm, which is robust and efficient, for fitting
per-atom scalar and vector quantities. The fingerprint is essentially a
continuous density field formed through the superimposition of smoothing
kernels centered on the atoms. Rotational invariance of the fingerprint is
achieved by aligning, for each fingerprint instance, the neighboring atoms onto
a local canonical coordinate frame computed from a kernel minisum optimization
procedure. We show that this approach is superior over PCA-based methods
especially when the atomistic neighborhood is sparse and/or contains symmetry.
We propose that the `distance' between the density fields be measured using a
volume integral of their pointwise difference. This can be efficiently computed
using optimal quadrature rules, which only require discrete sampling at a small
number of grid points. We also experiment on the choice of weight functions for
constructing the density fields, and characterize their performance for fitting
interatomic potentials. The applicability of the fingerprint is demonstrated
through a set of benchmark problems.