scholarly journals Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression

2016 ◽  
Vol 145 (17) ◽  
pp. 174112 ◽  
Author(s):  
Jonathan P. Alborzpour ◽  
David P. Tew ◽  
Scott Habershon
Keyword(s):  
Potential Energy ◽  
Gaussian Process ◽  
Quantum Dynamics ◽  
Gaussian Process Regression ◽  
Matrix Elements ◽  
Energy Matrix ◽  
Accurate Evaluation ◽  
Potential Energy Matrix

scholarly journals Influence of the Pauli principle on two-cluster potential energy

2020 ◽  
Author(s):  
Yuliya Lashko ◽  
Victor S. Vasilevsky ◽  
Gennady F. Filippov
Keyword(s):  
Potential Energy ◽  
Energy Operator ◽  
Pauli Principle ◽  
Matrix Elements ◽  
Energy Matrix ◽  
Eigenvalues And Eigenfunctions ◽  
Cluster Systems ◽  
Potential Energy Matrix ◽  
The Matrix ◽  
Trapped States

We study effects of the Pauli principle on the potential energy of two-cluster systems. The object of the investigation is the lightest nuclei of p-shell with a dominant \boldsymbol{\alpha}𝛂-cluster channel. For this aim we construct matrix elements of two-cluster potential energy between cluster oscillator functions with and without full antisymmetrization. Eigenvalues and eigenfunctions of the potential energy matrix are studied in detail. Eigenfunctions of the potential energy operator are presented in oscillator, coordinate and momentum spaces. We demonstrate that the Pauli principle affects more strongly the eigenfunctions than the eigenvalues of the matrix and leads to the formation of resonance and trapped states.

scholarly journals Direct quantum dynamics using variational Gaussian wavepackets and Gaussian process regression

2019 ◽  
Vol 150 (4) ◽  
pp. 041101 ◽  
Author(s):  
Iakov Polyak ◽  
Gareth W. Richings ◽  
Scott Habershon ◽  
Peter J. Knowles
Keyword(s):  
Gaussian Process ◽  
Quantum Dynamics ◽  
Gaussian Process Regression

scholarly journals Easy representation of multivariate functions with low-dimensional terms via Gaussian process regression kernel design: applications to machine learning of potential energy surfaces and kinetic energy densities from sparse data

2022 ◽  
Author(s):  
Sergei Manzhos ◽  
Eita Sasaki ◽  
Manabu Ihara
Keyword(s):  
Machine Learning ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Gaussian Process ◽  
Potential Energy Surfaces ◽  
Gaussian Process Regression ◽  
Multivariate Functions ◽  
Low Dimensional ◽  
Energy Surfaces ◽  
Kernel Design

Abstract We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with HDMR (High-dimensional model representation), one obtains a similar type of representation as the previously proposed HDMR-GPR scheme while being faster and simpler to use. We tested the approach on cases where highly accurate machine learning is required from sparse data by fitting potential energy surfaces and kinetic energy densities.

scholarly journals Ab initio instanton rate theory made efficient using Gaussian process regression

2018 ◽  
Vol 212 ◽  
pp. 237-258 ◽  
Author(s):  
Gabriel Laude ◽  
Danilo Calderini ◽  
David P. Tew ◽  
Jeremy O. Richardson
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Gaussian Process ◽  
Ab Initio ◽  
Energy Surface ◽  
Gaussian Process Regression ◽  
Rate Theory ◽  
Local Representation

In this paper, we describe how we use Gaussian process regression to fit a local representation of the potential energy surface and thereby obtain the instanton rate using only a small number of ab initio calculations.

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