The fitting of potential energy surfaces using neural networks: Application to the study of vibrational levels of H3+

Prudente, Frederico V.; Acioli, Paulo H.; Neto, J. J. Soares

doi:10.1063/1.477550

Cited by 115 publications

(89 citation statements)

References 33 publications

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“…Since the weights are all different, even exchanging the positions of any two chemically equivalent atoms changes the input vector G and thus the NN energy. It is possible to include this symmetry by defining symmetrized coordinates 28,36,41 or symmetric neurons, 44 but for large systems the construction of suitable coordinates becomes challenging.…”

Section: Neural Network Potentialsmentioning

confidence: 99%

High-dimensional neural network potentials for metal surfaces: A prototype study for copper

2012

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The atomic environments at metal surfaces differ strongly from the bulk, and, in particular, in case of reconstructions or imperfections at "real surfaces," very complicated atomic configurations can be present. This structural complexity poses a significant challenge for the development of accurate interatomic potentials suitable for large-scale molecular dynamics simulations. In recent years, artificial neural networks (NN) have become a promising new method for the construction of potential-energy surfaces for difficult systems. In the present work, we explore the applicability of such high-dimensional NN potentials to metal surfaces using copper as a benchmark system. A detailed analysis of the properties of bulk copper and of a wide range of surface structures shows that NN potentials can provide results of almost density functional theory (DFT) quality at a small fraction of the computational costs.

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Section: Neural Network Potentialsmentioning

confidence: 99%

High-dimensional neural network potentials for metal surfaces: A prototype study for copper

2012

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“…22 It has been observed 20 that the GA procedure, while rapidly converging at the beginning of the optimization, becomes slower in later stages due to GA's intrinsic difficulty in locating the exact optimum. In chemistry, they have been used successfully in rapidly characterizing ultrashort laser pulses, 25 fitting potential energy surfaces, [26][27][28][29] optimizing vibrational force fields, 17 recognizing patterns from various chemical sensors, [30][31][32] and interpreting circular dichroism 33 and IR ͑Ref. We extend this idea and utilize a deterministic optimizer not only in the final stage of the search, but also during the intermediate stages of optimization as described later in Sec.…”

Section: Introductionmentioning

confidence: 99%

Application of artificial neural networks and genetic algorithms to modeling molecular electronic spectra in solution

Lilichenko

Kelley

2001

The Journal of Chemical Physics

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Improving the accuracy of density-functional theory calculation: The genetic algorithm and neural network approach A novel approach is presented for finding the vibrational frequencies, Franck-Condon factors, and vibronic linewidths that best reproduce typical, poorly resolved electronic absorption ͑or fluorescence͒ spectra of molecules in condensed phases. While calculation of the theoretical spectrum from the molecular parameters is straightforward within the harmonic oscillator approximation for the vibrations, ''inversion'' of an experimental spectrum to deduce these parameters is not. Standard nonlinear least-squares fitting methods such as Levenberg-Marquardt are highly susceptible to becoming trapped in local minima in the error function unless very good initial guesses for the molecular parameters are made. Here we employ a genetic algorithm to force a broad search through parameter space and couple it with the Levenberg-Marquardt method to speed convergence to each local minimum. In addition, a neural network trained on a large set of synthetic spectra is used to provide an initial guess for the fitting parameters and to narrow the range searched by the genetic algorithm. The combined algorithm provides excellent fits to a variety of single-mode absorption spectra with experimentally negligible errors in the parameters. It converges more rapidly than the genetic algorithm alone and more reliably than the Levenberg-Marquardt method alone, and is robust in the presence of spectral noise. Extensions to multimode systems, and/or to include other spectroscopic data such as resonance Raman intensities, are straightforward.

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“…It is possible to use symmetrized neurons in the first hidden layer (e.g., the NN potential for H 1 3 [37] ) of a multilayer NN. An NN can also be symmetrized by imposing conditions on the weights (e.g., PESs for H 2 O and ClOOCl [61] ).…”

Section: Symmetry Issuesmentioning

confidence: 99%

“…[31,32] When a simple NN is used the fitting procedure is straightforward. [23,[37][38][39][40][41][42] Fitting to sums of NNs, that is, increasing the complexity of the network, is advantageous when either high accuracy is required or the density of the fitting points is low (often due to high dimensionality). The purpose of the present review, in contrast to the available reviews, is not to list examples of NN PESs but to describe more complex NN methods that two of the authors (S. M. and T. C.) developed and specifically, their evolution from simple NNs toward more complex structures.…”

Section: Introductionmentioning

confidence: 99%

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

Manzhos

Dawes

Carrington

2014

Int J of Quantum Chemistry

198

148

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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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The fitting of potential energy surfaces using neural networks: Application to the study of vibrational levels of H3+

Cited by 115 publications

References 33 publications

High-dimensional neural network potentials for metal surfaces: A prototype study for copper

High-dimensional neural network potentials for metal surfaces: A prototype study for copper

Application of artificial neural networks and genetic algorithms to modeling molecular electronic spectra in solution

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

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