Applications of neural networks to fitting interatomic potential functions

Hobday, Steven; Smith, Roger; Belbruno, Joe

doi:10.1088/0965-0393/7/3/308

Cited by 44 publications

(43 citation statements)

References 10 publications

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“…Nevertheless, several interesting and quite successful attempts have also been made in this early stage to extend the applicability of NNs to systems including larger numbers of atoms. 45,46 Starting with NNs 32 in 2007, several different ML approaches suitable for high-dimensional systems containing thousands of atoms have now become available 38,40 and are still evolving rapidly. 10,47,48 An overview about the increasing use of different ML techniques to the construction of PESs is shown in Fig.…”

Section: A Overviewmentioning

confidence: 99%

Perspective: Machine learning potentials for atomistic simulations

Behler

2016

The Journal of Chemical Physics

1,184

955

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Nowadays, computer simulations have become a standard tool in essentially all fields of chemistry, condensed matter physics, and materials science. In order to keep up with state-of-the-art experiments and the ever growing complexity of the investigated problems, there is a constantly increasing need for simulations of more realistic, i.e., larger, model systems with improved accuracy. In many cases, the availability of sufficiently efficient interatomic potentials providing reliable energies and forces has become a serious bottleneck for performing these simulations. To address this problem, currently a paradigm change is taking place in the development of interatomic potentials. Since the early days of computer simulations simplified potentials have been derived using physical approximations whenever the direct application of electronic structure methods has been too demanding. Recent advances in machine learning (ML) now offer an alternative approach for the representation of potential-energy surfaces by fitting large data sets from electronic structure calculations. In this perspective, the central ideas underlying these ML potentials, solved problems and remaining challenges are reviewed along with a discussion of their current applicability and limitations. Published by AIP Publishing. [http://dx

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Section: A Overviewmentioning

confidence: 99%

Perspective: Machine learning potentials for atomistic simulations

Behler

2016

The Journal of Chemical Physics

1,184

955

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“…The neural network model variable description r ij length of bond i − j r jk length of bond j − k cos θ ijk cosine of angle between bonds i − j and j − k r kl length of bond k − l cos θ jkl cosine of angle between bonds j − k and k − l cos τ ijkl cosine of torsion angle between bonds i − j and k − l N i = i =j S ij sum of screening present over every bond i − j formed per atom i N j = i =j,j =k S jk sum of screening present over every bond j − k formed per atom j The neural network is developed in such a way that the input layer can vary with the number of 4-atom chains that can be formed. This is non-standard and was previously used by our group in the Tersoff potential fitting [9]. In addition the potential is constructed to be a continuous function of the input variables and invariant to the ordering of the inputs.…”

Section: A the Variables For The Problemmentioning

confidence: 99%

“…Another approach had also been suggested at the COSIRES meeting held at Pennsylvania State University [8,9] through the use of neural networks (NN's) to fit the potential energy surface. In that case only the feasibility of the method was examined showing how the many-body term in the Tersoff potential could be fitted by a neural network whose inputs depended only on the local geometry of an Si atom.…”

Section: Introductionmentioning

confidence: 99%

A new approach to potential fitting using neural networks

Bholoa

Kenny

Smith

2007

Nuclear Instruments and Methods in Physics Research Section B:

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A new approach to potential fitting using neural networks The NN model successfully fitted energy variations of the different test cases as a function of bond distances, bond angles, lattice constants and elastic properties for both equilibrium and non-equilibrium small cluster and bulk structures. This indicates a robust and consistent methodology for fitting empirical potentials which can be applied to a wide range of materials independent of the type of bonding or their crystal structure.

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“…Most of these NN potentials, however, are restricted to small molecules [26][27][28][29][30][31][32] or small molecules interacting with frozen metal surfaces [33][34][35][36][37][38]. Only a few potentials for higher-dimensional systems exist, which aim to describe the properties of solids [39,40].…”

Section: Introductionmentioning

confidence: 99%

A Full-Dimensional Neural Network Potential-Energy Surface for Water Clusters up to the Hexamer

Morawietz

Behler

2013

Zeitschrift Für Physikalische Chemie

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Water clusters have attracted a lot of attention as prototype systems to study hydrogen bonded molecular aggregates but also to gain deeper insights into the properties of liquid water, the solvent of life. All these studies depend on an accurate description of the atomic interactions and countless potentials have been proposed in the literature in the past decades to represent the potential-energy surface (PES) of water. Many of these potentials employ drastic approximations like rigid water monomers and fixed point charges, while on the other hand also several attempts have been made to derive very accurate PESs by fitting data obtained in high-level electronic structure calculations. In recent years artificial neural networks (NNs) have been established as a powerful tool to construct high-dimensional PESs of a variety of systems, but to date no full-dimensional NN PES for water has been reported. Here, we present NN potentials for water clusters containing two to six water molecules trained to density functional theory (DFT) data employing two different exchange-correlation functionals, PBE and RPBE. In contrast to other potentials fitted to first principles data, these NN potentials are not based on a truncated many-body expansion of the energy but consider the interactions between all water molecules explicitly. For both functionals an excellent agreement with the underlying DFT calculations has been found with binding energy errors of only about 1%.

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Applications of neural networks to fitting interatomic potential functions

Cited by 44 publications

References 10 publications

Perspective: Machine learning potentials for atomistic simulations

Perspective: Machine learning potentials for atomistic simulations

A new approach to potential fitting using neural networks

A Full-Dimensional Neural Network Potential-Energy Surface for Water Clusters up to the Hexamer

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