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The atomic cluster expansion (ACE) has been highly successful for the parameterisation of symmetric (invariant or equivariant) properties of many-particle systems. Here, we generalize its derivation to anti-symmetric functions. We show how…
The Atomic Cluster Expansion (ACE) (Drautz, Phys. Rev. B 99, 2019) has been widely applied in high energy physics, quantum mechanics and atomistic modeling to construct many-body interaction models respecting physical symmetries.…
We present an atomic cluster expansion (ACE) for carbon that improves over available classical and machine learning potentials. The ACE is parameterized from an exhaustive set of important carbon structures at extended volume and energy…
Machine learning interatomic potentials are revolutionizing large-scale, accurate atomistic modelling in material science and chemistry. Many potentials use atomic cluster expansion or equivariant message passing frameworks. Such frameworks…
The Atomic Cluster Expansion (ACE) [R. Drautz, Phys. Rev. B, 99:014104 (2019)] provides a systematically improvable, universal descriptor for the environment of an atom that is invariant to permutation, translation and rotation. ACE is…
Atomic cluster expansion (ACE) methods provide a systematic way to describe particle local environments of arbitrary body order. For practical applications it is often required that the basis of cluster functions be symmetrized with respect…
Traditionally, interatomic potentials assume local bond formation supplemented by long-range electrostatic interactions when necessary. This ignores intermediate range multi-atom interactions that arise from the relaxation of the electronic…
``Extended Ensemble Monte Carlo''is a generic term that indicates a set of algorithms which are now popular in a variety of fields in physics and statistical information processing. Exchange Monte Carlo (Metropolis-Coupled Chain, Parallel…
We derive an adaptive hierarchical method of estimating high dimensional probability density functions. We call this method of density estimation the "adaptive cluster expansion" or ACE for short. We present an application of this approach,…
A numerically implementable Multi-scale Many-Body approach to strongly correlated electron systems is introduced. An extension to quantum cluster methods, it approximates correlations on any given length-scale commensurate with the strength…
We present a highly accurate and transferable parameterization of water using the atomic cluster expansion (ACE). To efficiently sample liquid water, we propose a novel approach that involves sampling static calculations of various ice…
The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code \verb+PACE+ that is suitable for use in large scale…
We present a general-purpose parameterization of the atomic cluster expansion (ACE) for magnesium. The ACE shows outstanding transferability over a broad range of atomic environments and captures physical properties of bulk as well as…
Using the maximum entropy method, we derive the "adaptive cluster expansion" (ACE), which can be trained to estimate probability density functions in high dimensional spaces. The main advantage of ACE over other Bayesian networks is its…
We introduce a novel many body method which combines two powerful many body techniques, viz., quantum Monte Carlo and coupled cluster theory. Coupled cluster wave functions are introduced as importance functions in a Monte Carlo method…
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…
This paper extends the Multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, Multilevel Monte Carlo is applied to a certain variant of the particle filter, the Ensemble Transform Particle Filter. A key…
The silicon-hydrogen system is of key interest for solar-cell devices, including both crystalline and amorphous modifications. Elemental amorphous Si is now well understood, but the atomic-scale effects of hydrogenating the silicon matrix…
We study the convergence of a linear atomic cluster expansion (ACE) potential with respect to its basis functions, in terms of the effective two-body interactions of elemental Carbon and Silicon systems. We build ACE potentials with…
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 interatomic potential requires a careful selection of training…