Chemical compound space (CCS), the set of all theoretically conceivable combinations of
chemical elements and (meta-) stable geometries that make up matter, is colossal. The first …

During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …

The subject of this paper is the technology (the'how') of constructing machine-learning
interatomic potentials, rather than science (the'what'and'why') of atomistic simulations using …

This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …

This paper introduces an active learning approach to the fitting of machine learning
interatomic potentials. Our approach is based on the D-optimality criterion for selecting …

We use tensor network techniques to obtain high-order perturbative diagrammatic
expansions for the quantum many-body problem at very high precision. The approach is …

As is well known, a rank-r matrix can be recovered from a cross of r linearly independent
columns and rows, and an arbitrary matrix can be interpolated on the cross entries. Other …

Low rank approximation of matrices has been well studied in literature. Singular value
decomposition, QR decomposition with column pivoting, rank revealing QR factorization …

In recent years, the machine learning techniques have shown great potent1ial in various
problems from a multitude of disciplines, including materials design and drug discovery. The …

The atomic cluster expansion (ACE) was proposed recently as a new class of data-driven
interatomic potentials with a formally complete basis set. Since the development of any …