# Performant implementation of the atomic cluster expansion (PACE) and application to copper and silicon

@article{Lysogorskiy2021PerformantIO, title={Performant implementation of the atomic cluster expansion (PACE) and application to copper and silicon}, author={Yury Lysogorskiy and Cas van der Oord and A. V. Bochkarev and Sarath Menon and Matteo Rinaldi and Thomas Hammerschmidt and Matous Mrovec and Aidan Thompson and G{\'a}bor Cs{\'a}nyi and Christoph Ortner and Ralf Drautz}, journal={npj Computational Materials}, year={2021}, volume={7}, pages={1-12} }

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 PACE that is suitable for use in large-scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in PACE shifts a…

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## References

SHOWING 1-10 OF 80 REFERENCES

Atomic cluster expansion: Completeness, efficiency and stability

- Mathematics, Computer ScienceJournal of Computational Physics
- 2022

A fast recursive algorithm is provided for efficient evaluation of the derivation of polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling properties of atomistic systems.

Quantum-accurate spectral neighbor analysis potential models for Ni-Mo binary alloys and fcc metals

- Physics, Materials SciencePhysical Review B
- 2018

In recent years, efficient interatomic potentials approaching the accuracy of density functional theory (DFT) calculations have been developed using rigorous atomic descriptors satisfying strict…

A Performance and Cost Assessment of Machine Learning Interatomic Potentials.

- Medicine, ChemistryThe journal of physical chemistry. A
- 2020

A comprehensive evaluation of ML-IAPs based on four local environment descriptors --- atom-centered symmetry functions (ACSF), smooth overlap of atomic positions (SOAP), the Spectral Neighbor Analysis Potential (SNAP) bispectrum components, and moment tensors --- using a diverse data set generated using high-throughput density functional theory (DFT) calculations.

Regularised atomic body-ordered permutation-invariant polynomials for the construction of interatomic potentials

- Computer Science, MathematicsMach. Learn. Sci. Technol.
- 2020

It is shown that the low dimensionality combined with careful regularisation actually leads to better transferability than the high dimensional, kernel based Gaussian Approximation Potential.

Machine Learning a General-Purpose Interatomic Potential for Silicon

- Materials Science, PhysicsPhysical Review X
- 2018

The success of first principles electronic structure calculation for predictive modeling in chemistry, solid state physics, and materials science is constrained by the limitations on simulated length…

Atom-centered symmetry functions for constructing high-dimensional neural network potentials.

- Physics, MedicineThe Journal of chemical physics
- 2011

Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces and a transformation to symmetry functions is required to enable molecular dynamics simulations of large systems.

Efficient O(N) integration for all-electron electronic structure calculation using numeric basis functions

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2009

It is shown that a conceptually simple top-down grid partitioning scheme achieves essentially the same efficiency as the more rigorous bottom-up approaches.

Generalized neural-network representation of high-dimensional potential-energy surfaces.

- Computer Science, MedicinePhysical review letters
- 2007

A new kind of neural-network representation of DFT potential-energy surfaces is introduced, which provides the energy and forces as a function of all atomic positions in systems of arbitrary size and is several orders of magnitude faster than DFT.

Structural stability and lattice defects in copper: Ab initio , tight-binding, and embedded-atom calculations

- Materials Science
- 2001

We evaluate the ability of the embedded-atom method ~EAM! potentials and the tight-binding ~TB! method to predict reliably energies and stability of nonequilibrium structures by taking Cu as a model…

On representing chemical environments

- Physics
- 2013

We review some recently published methods to represent atomic neighborhood environments, and analyze their relative merits in terms of their faithfulness and suitability for fitting potential energy…