Artificial neural network potentials
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[edit]
Training[edit]
Example[edit]
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[edit]
Since the early work of Blank et al. [3] ANNS have been sucessfully developed for water [4], Al3+ ions dissolved in water [5], aqueous NaOH solutions [6], gold nanoparticles [7] as well as many other systems [8][9].
References[edit]
- ↑ 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)
- Caroline Desgranges and Jerome Delhommelle "A new approach for the prediction of partition functions using machine learning techniques", Journal of Chemical Physics 149, 044118 (2018)