Representing Global Reactive Potential Energy Surfaces Using Gaussian Processes

Kolb, Brian; Marshall, Paul; Zhao, Bin; Jiang, Bin; Guo, Hua

doi:10.1021/acs.jpca.7b01182

Cited by 81 publications

(77 citation statements)

References 46 publications

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“…In all previous studies [21][22][23][24][25][26][27][28][29][30], the GP models of PES were constructed with a fixed kernel function, such as one of the kernel functions (3) - (5). In the present work, we follow…”

Section: Composite Kernels For Gp Models Of Pesmentioning

confidence: 99%

Interpolation and Extrapolation of Global Potential Energy Surfaces for Polyatomic Systems by Gaussian Processes with Composite Kernels

Dai

Krems

2020

J. Chem. Theory Comput.

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Gaussian process regression has recently emerged as a powerful, system-agnostic tool for building global potential energy surfaces (PES) of polyatomic molecules. While the accuracy of GP models of PES increases with the number of potential energy points, so does the numerical difficulty of training and evaluating GP models. Here, we demonstrate an approach to improve the accuracy of global PES without increasing the number of energy points. The present work reports four important results. First, we show that the selection of the best kernel function for GP models of PES can be automated using the Bayesian information criterion as a model selection metric.Second, we demonstrate that GP models of PES trained by a small number of energy points can be significantly improved by iteratively increasing the complexity of GP kernels. The composite kernels thus obtained maximize the accuracy of GP models for a given distribution of potential energy points. Third, we show that the accuracy of the GP models of PES with composite kernels can be further improved by varying the training point distributions. Fourth, we show that GP models with composite kernels can be used for physical extrapolation of PES. We illustrate the approach by constructing the six-dimensional PES for H 3 O + . For the interpolation problem, we show that this algorithm produces a global six-dimensional PES for H 3 O + in the energy range between zero and 21, 000 cm −1 with the root mean square error 65.8 cm −1 using only 500 randomly selected ab initio points as input. To illustrate extrapolation, we produce the PES at high energies using the energy points at low energies as input. We show that one can obtain an accurate global fit of the PES extending to 21, 000 cm −1 based on 1500 potential energy points at energies below 10, 000 cm −1 . arXiv:1907.08717v1 [physics.chem-ph]

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Section: Composite Kernels For Gp Models Of Pesmentioning

confidence: 99%

Interpolation and Extrapolation of Global Potential Energy Surfaces for Polyatomic Systems by Gaussian Processes with Composite Kernels

Dai

Krems

2020

J. Chem. Theory Comput.

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“…where E i are the ab initio energy points and the weights (w i ) are determined by the two-tiered GP model to yield the best outcome of the quantum scattering calculation. GPs have been previously used for interpolating PES for molecular dynamics applications [12][13][14][15][16], spectroscopic line calculations [17,18] and molecular scattering calculations [19,20]. We emphasize that equation (3) is not a fit of the PES but a non-parametric regression.…”

Section: Gp Regression For Pesmentioning

confidence: 99%

Bayesian optimization for the inverse scattering problem in quantum reaction dynamics

et al. 2019

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We propose a machine-learning approach based on Bayesian optimization to build global potential energy surfaces (PES) for reactive molecular systems using feedback from quantum scattering calculations. The method is designed to correct for the uncertainties of quantum chemistry calculations and yield potentials that reproduce accurately the reaction probabilities in a wide range of energies. These surfaces are obtained automatically and do not require manual fitting of the ab initio energies with analytical functions. The PES are built from a small number of ab initio points by an iterative process that incrementally samples the most relevant parts of the configuration space. Using the dynamical results of previous authors as targets, we show that such feedback loops produce accurate global PES with 30 ab initio energies for the three-dimensional H+H 2  H 2 + H reaction and 290 ab inito energies for the six-dimensional OH + H 2  H 2 O+H reaction. These surfaces are obtained from 360 scattering calculations for H 3 and 600 scattering calculations for OH 3 . We also introduce a method that quickly converges to an accurate PES without the a priori knowledge of the dynamical results. By construction, our method illustrates the lowest number of potential energy points (i.e. the minimum information) required for the non-parametric construction of global PES for quantum reactive scattering calculations.

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“…For example, the same code without any additional programming effort can be applied to construct a PES for systems with different atoms (e.g., RbCs vs NaK) and, even, with different dimensions (e.g., NaK-NaK vs Na-NaK). As shown recently, [14][15][16][17][18] GP regression can produce accurate PESs for polyatomic systems with a small number of ab initio points. However, as any ML method, GP regression is designed for interpolation and cannot extrapolate outside the range of available ab initio energy points.…”

Section: Introductionmentioning

confidence: 75%

“…The resulting expressions enter Eqs. (14) and (15) GP 14 ( x), and V GP 23 ( x). Figure 2 shows the result of the procedure described above for a sample orientation.…”

Section: E Merging the Short Range And The Long Rangementioning

confidence: 99%

Six-dimensional potential energy surface for NaK–NaK collisions: Gaussian process representation with correct asymptotic form

Christianen¹,

Karman

Vargas-Hernández

et al. 2019

The Journal of Chemical Physics

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Constructing accurate global potential energy surfaces (PESs) describing chemically reactive molecule-molecule collisions of alkali metal dimers presents a major challenge. To be suitable for quantum scattering calculations, such PESs must represent accurately three-and four-body interactions, describe conical intersections, and have a proper asymptotic form at the long range. Here, we demonstrate that such global potentials can be obtained by Gaussian Process (GP) regression merged with the analytic asymptotic expansions at the long range. We propose an efficient sampling technique, which allows us to construct an accurate global PES accounting for different chemical arrangements with <2500 ab initio calculations. We apply this method to (NaK) 2 and obtain the first global PES for a system of four alkali metal atoms. The resulting surface exhibits a complex landscape including a pair and a quartet of symmetrically equivalent local minima and a seam of conical intersections. The dissociation energy found from our ab initio calculations is 4534 cm −1. This result is reproduced by the GP models with an error of less than 3%. The GP models of the PES allow us to analyze the features of the global PES, representative of general alkali metal four-atom interactions. Understanding these interactions is of key importance in the field of ultracold chemistry.

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Representing Global Reactive Potential Energy Surfaces Using Gaussian Processes

Cited by 81 publications

References 46 publications

Interpolation and Extrapolation of Global Potential Energy Surfaces for Polyatomic Systems by Gaussian Processes with Composite Kernels

Interpolation and Extrapolation of Global Potential Energy Surfaces for Polyatomic Systems by Gaussian Processes with Composite Kernels

Bayesian optimization for the inverse scattering problem in quantum reaction dynamics

Six-dimensional potential energy surface for NaK–NaK collisions: Gaussian process representation with correct asymptotic form

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