Using neural networks to represent potential surfaces as sums of products

Manzhos, Sergei; Carrington, Tucker

doi:10.1063/1.2387950

Cited by 176 publications

(150 citation statements)

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“…Fitting potential energy surfaces (PESs) and electrostatic multipole moment surfaces of small molecules to data generated by first principles electronic structure calculations has been a mainstay of computational chemistry for decades 7,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] . Typically, when modelling the PES of a small group of atoms, the list of pairwise distances is used or, equivalently, some transformed version of the interatomic distances, e.g.…”

Section: Introductionmentioning

confidence: 99%

On representing chemical environments

2013

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We review some recently published methods to represent atomic neighbourhood environments, and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms, and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave numbers are used to expand the atomic neighbourhood density function. Using the example system of small clusters, we quantitatively show that this expansion needs to be carried to higher and higher wave numbers as the number of neighbours increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether new approach, called Smooth Overlap of Atomic Positions (SOAP), that sidesteps these difficulties by directly defining the similarity between any two neighbourhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.

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Section: Introductionmentioning

confidence: 99%

On representing chemical environments

2013

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“…of terms represented PES by the choice of the neuron. Specifically, using a simple exponential function, g x ð Þ5e x together with g out x ð Þ5x, a SOP form is easily obtained (which we call expnn [108] ):…”

Section: Transformed Coordinates and Dimensionality Reductionmentioning

confidence: 99%

“…The error of the expnn PES is comparable to the cumulative error of the original 1 potfit fits. [25,26,108] Brown and coworkers have used expnn to fit a PES of CS 2 to highly accurate ab initio data and to compute its vibrational levels. [117] They also showed that expnn can be interfaced with the multiconfiguration time dependent Hartree algorithm.…”

Section: Transformed Coordinates and Dimensionality Reductionmentioning

confidence: 99%

“…[22] It has been demonstrated that NN PESs are very accurate for small molecules and as good as other methods for larger molecules. [23][24][25][26][27][28][29][30][31][32] If used with exponential neurons [108] or with product neurons, [33] they yield PESs in sum-of-products (SOP) form. The SOP form facilitates quantum dynamics calculations.…”

Section: Introductionmentioning

confidence: 99%

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Neural network‐based approaches for building high dimensional and quantum dynamics‐friendly potential energy surfaces

Manzhos

Dawes

Carrington

2014

Int J of Quantum Chemistry

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Development and applications of neural network (NN)-based approaches for representing potential energy surfaces (PES) of bound and reactive molecular systems are reviewed. Specifically, it is shown that when the density of ab initio points is low, NNs-based potentials with multibody or multimode structure are advantageous for representing high-dimensional PESs. Importantly, with an appropriate choice of the neuron activation function, PESs in the sum-of-products form are naturally obtained, thus addressing a bottleneck problem in quantum dynamics. The use of NN committees is also analyzed and it is shown that while they are able to reduce the fitting error, the reduction is limited by the nonrandom nature of the fitting error. The approaches described here are expected to be directly applicable in other areas of science and engineering where a functional form needs to be constructed in an unbiased way from sparse data.

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“…PES can be forced into SOPs form by using, for example, potfit [5,97], multigrid potfit [98], or neural network methods [99][100][101].…”

Section: Using Rank Reduction To Avoid Storing Full Dimensional Vectorsmentioning

confidence: 99%

Iterative Methods for Computing Vibrational Spectra

Carrington

2018

Mathematics

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I review some computational methods for calculating vibrational spectra. They all use iterative eigensolvers to compute eigenvalues of a Hamiltonian matrix by evaluating matrix-vector products (MVPs). A direct-product basis can be used for molecules with five or fewer atoms. This is done by exploiting the structure of the basis and the structure of a direct product quadrature grid. I outline three methods that can be used for molecules with more than five atoms. The first uses contracted basis functions and an intermediate (F) matrix. The second uses Smolyak quadrature and a pruned basis. The third uses a tensor rank reduction scheme.

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Using neural networks to represent potential surfaces as sums of products

Cited by 176 publications

References 50 publications

On representing chemical environments

On representing chemical environments

Neural network‐based approaches for building high dimensional and quantum dynamics‐friendly potential energy surfaces

Iterative Methods for Computing Vibrational Spectra

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