Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Atomic Cluster Expansion: Completeness, Efficiency and Stability   The Atomic Cluster Expansion (Drautz, Phys. Rev. B 99, 2019) provides a
framework to systematically derive polynomial basis functions for approximating
isometry and permutation invariant functions, particularly with an eye to
modelling properties of atomistic systems. Our presentation extends the
derivation by proposing a precomputation algorithm that yields immediate
guarantees that a complete basis is obtained. We provide a fast recursive
algorithm for efficient evaluation and illustrate its performance in numerical
tests. Finally, we discuss generalisations and open challenges, particularly
from a numerical stability perspective, around basis optimisation and parameter
estimation, paving the way towards a comprehensive analysis of the convergence
to a high-fidelity reference model.

23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph