# Difference between revisions of "Artificial neural network potentials"

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*[http://dx.doi.org/10.1002/qua.24890 Jörg Behler "Constructing high-dimensional neural network potentials: A tutorial review", International Journal of Quantum Chemistry '''115''' pp. 1032-1050 (2015)] | *[http://dx.doi.org/10.1002/qua.24890 Jörg Behler "Constructing high-dimensional neural network potentials: A tutorial review", International Journal of Quantum Chemistry '''115''' pp. 1032-1050 (2015)] | ||

*[http://dx.doi.org/10.1063/1.4966192 Jörg Behler "Perspective: Machine learning potentials for atomistic simulations", Journal of Chemical Physics '''145''' 170901 (2016)] | *[http://dx.doi.org/10.1063/1.4966192 Jörg Behler "Perspective: Machine learning potentials for atomistic simulations", Journal of Chemical Physics '''145''' 170901 (2016)] | ||

+ | *[https://doi.org/10.1063/1.5027645 Linfeng Zhang, Jiequn Han, Han Wang, Roberto Car, and Weinan E "DeePCG: Constructing coarse-grained models via deep neural networks", Journal of Chemical Physics '''149''' 034101 (2018)] | ||

[[category:models]] | [[category:models]] |

## Revision as of 16:06, 23 July 2018

**Artificial neural network potentials** (ANNP). Neural networks (NN) are used more and more for a wide array of applications. Here we are concerned with a more narrow application; their use in fitting
^{[1]}
^{[2]} to an atomic or molecular potential energy surface. In particular the *output layer*, or *node*, provides an energy as a function of the coordinates, which form the *input layer*.

## Activation functions

## Training

## Example

The output of a feedforward NN, having a single layer of hidden neurons, each having a sigmoid activation function and a linear output neuron, is given by:

## Applications

Since the early work of Blank *et al*. ^{[3]} ANNS have been sucessfully developed for water ^{[4]},
Al^{3+} ions dissolved in water ^{[5]},
aqueous NaOH solutions ^{[6]},
gold nanoparticles ^{[7]} as well as many other systems ^{[8]}^{[9]}.

## References

- ↑ G. Cybenko "Approximation by superpositions of a sigmoidal function", Mathematics of Control, Signals and Systems
**2**pp. 303-314 (1989) - ↑ Kurt Hornik, Maxwell Stinchcombe, Halbert White "Multilayer feedforward networks are universal approximators", Neural Networks
**2**pp. 359-366 (1989) - ↑ Thomas B. Blank, Steven D. Brown, August W. Calhoun, and Douglas J. Doren "Neural network models of potential energy surfaces", Journal of Chemical Physics
**103**4129 (1995) - ↑ Tobias Morawietz, Andreas Singraber, Christoph Dellago, and Jörg Behler "How van der Waals interactions determine the unique properties of water", PNAS
**113**pp. 8368-8373 (2016) - ↑ Helmut Gassner, Michael Probst, Albert Lauenstein, and Kersti Hermansson "Representation of Intermolecular Potential Functions by Neural Networks", Journal of Physical Chemistry A
**102**pp. 4596-4605 (1998) - ↑ Matti Hellström and Jörg Behler "Structure of aqueous NaOH solutions: insights from neural-network-based molecular dynamics simulations", Physical Chemistry Chemical Physics
**19**pp. 82-96 (2017) - ↑ Siva Chiriki, Shweta Jindal, and Satya S. Bulusu "Neural network potentials for dynamics and thermodynamics of gold nanoparticles", Journal of Chemical Physics
**146**084314 (2017) - ↑ Sönke Lorenz, Axel Groß and Matthias Scheffler "Representing high-dimensional potential-energy surfaces for reactions at surfaces by neural networks", Chemical Physics Letters
**395**pp. 210-215 (2004) - ↑ Sergei Manzhos, Xiaogang Wang, Richard Dawes, and Tucker Carrington Jr. "A Nested Molecule-Independent Neural Network Approach for High-Quality Potential Fits", Journal of Physical Chemistry A
**110**pp. 5295-5304 (2006)

- Related reading

- Christopher Michael Handley and Jörg Behler "Next generation interatomic potentials for condensed systems", European Physical Journal B
**87**152 (2014) - Jörg Behler "Constructing high-dimensional neural network potentials: A tutorial review", International Journal of Quantum Chemistry
**115**pp. 1032-1050 (2015) - Jörg Behler "Perspective: Machine learning potentials for atomistic simulations", Journal of Chemical Physics
**145**170901 (2016) - Linfeng Zhang, Jiequn Han, Han Wang, Roberto Car, and Weinan E "DeePCG: Constructing coarse-grained models via deep neural networks", Journal of Chemical Physics
**149**034101 (2018)