Artificial neural network potentials: Difference between revisions
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'''Artificial neural network potentials''' (ANNP) | '''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== | ==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: | 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: | ||
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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== | ||
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)] | [[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> | </ref> | ||
Revision as of 13:14, 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:
![{\displaystyle 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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/838a0027d3aef6bb8b9b13f90b3490e2ffd26842)
Applications
Since the early work of Blank et al. [1] ANNS have been sucessfully developed for water [2] aqueous NaOH solutions [3] gold nanoparticles [4].
References
- ↑ 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)
- ↑ 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)
- 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)