Artificial neural network potentials: Difference between revisions

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:<math>g(\mathbf{x},\mathbf{w}) = \sum_{i=1}^{N_c} \left[  w_{N_C+1,i} \tanh  \left( \sum_{j=1}^n w_{i,j} x_j + w_{i0} \right)  \right] + w_{N_c+1,0} </math>
:<math>g(\mathbf{x},\mathbf{w}) = \sum_{i=1}^{N_c} \left[  w_{N_C+1,i} \tanh  \left( \sum_{j=1}^n w_{i,j} x_j + w_{i0} \right)  \right] + w_{N_c+1,0} </math>
==Applications==
==Applications==
Since the early work of Blank ''et al. <ref>[http://dx.doi.org/10.1063/1.469597 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)]</ref> ANNS have been sucessfully developed for [[water]] <ref>[http://dx.doi.org/10.1073/pnas.1602375113 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)]</ref>
Since the early work of Blank ''et al''. <ref>[http://dx.doi.org/10.1063/1.469597 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)]</ref> ANNS have been sucessfully developed for [[water]] <ref>[http://dx.doi.org/10.1073/pnas.1602375113 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)]</ref>,
[[Sodium hydroxide-water mixture | aqueous NaOH solutions]] <ref>[http://dx.doi.org/10.1039/C6CP06547C 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)]
Al<sup>3+</sup> ions dissolved in water <ref>[http://dx.doi.org/10.1021/jp972209d 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)]</ref>,
</ref>
[[Sodium hydroxide-water mixture | aqueous NaOH solutions]] <ref>[http://dx.doi.org/10.1039/C6CP06547C 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)]</ref>,
[[gold]] nanoparticles <ref>[http://dx.doi.org/10.1063/1.4977050 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)]</ref>.
[[gold]] nanoparticles <ref>[http://dx.doi.org/10.1063/1.4977050 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)]</ref> as well as may other systems <ref>[http://dx.doi.org/10.1016/j.cplett.2004.07.076 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)]</ref><ref>[http://dx.doi.org/10.1021/jp055253z 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)]</ref>.
==References==
==References==
<references/>
<references/>

Revision as of 14:42, 17 March 2017

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. In particular the output layer, or node, provides an energy as a function of the input layer.

Activation functions

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. [1] ANNS have been sucessfully developed for water [2], Al3+ ions dissolved in water [3], aqueous NaOH solutions [4], gold nanoparticles [5] as well as may other systems [6][7].

References

  1. ↑ 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)
  2. ↑ 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)
  3. ↑ 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)
  4. ↑ 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)
  5. ↑ 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)
  6. ↑ 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)
  7. ↑ 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)
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