Evaluation of pairwise distances among orthogonal grid points in hypercube

Sadílek, Václav; Vořechovský, Miroslav; Šmídová, Magdalena

doi:10.1063/1.4992284

Cited by 4 publications

(3 citation statements)

References 4 publications

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“…In higher dimensions N var 3 , the exponent l = 2 further leads to convergence of the potential energy to a constant [12]. Using the above proposed exponent l = N var + 1, the potential energy value tends to a power law as…”

Section: The Exponent Lmentioning

confidence: 93%

“…In the original AE criterion and also in the periodic version (PAE), the potential energy between each pair of points is not dependent on the dimension, N var . It has been found [12] that the character of the criterion is different for various N var and also for various numbers of points, N sim . In 1D situation, the energy tends to infinity linearly with increasing N sim .…”

Section: The Exponent Lmentioning

confidence: 99%

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Formulation of Potential for Dynamical Particle System Applied to Monte Carlo Sampling

Masek¹,

Vořechovský²

2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. The presented paper investigates the effect of formulation of energy potential of a dynamical particle system as used for optimization of statistical point sampling. The dynamical particle system, originally developed as a physical analogy of the Audze-Eglajs (AE) optimization criterion and its periodical modification (PAE), effectively demonstrated that the originally proposed potential performs well only in poorly applicable scenarios of design spaces of low dimension filled with rather high number of design points. A remedy lying in a refined formulation of energy potential as well as its derivation and reasoning are presented.

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Section: The Exponent Lmentioning

confidence: 93%

Section: The Exponent Lmentioning

confidence: 99%

Formulation of Potential for Dynamical Particle System Applied to Monte Carlo Sampling

Masek¹,

Vořechovský²

2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the original AE criterion and also in the periodic version (PAE), the potential energy between each pair of points is not dependent on the dimension, var N . It has been found [12] that the character of the criterion is different for various var N and also for various numbers of points, sim N . In the 1D situation, the energy tends to infinity linearly with increasing sim N .…”

Section: The Exponentmentioning

confidence: 99%

On the Influence of the Interaction Laws of a Dynamical Particle System for Sample Optimization

Masek¹,

Vořechovský²

2017

Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series.

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The presented paper investigates the effect of the formulation of the energy potential of a dynamical particle system used for the optimization of statistical point sampling. The dynamical particle system, originally developed as a physical analogy to the Audze-Eglajs (AE) optimization criterion and its periodical modification (PAE), effectively demonstrated that the originally proposed energy potential performs well only in poorly applicable scenarios featuring low-dimensional design domains filled with a rather high number of design points. A remedy is presented which involves a refined formulation of the energy potential, as well as its derivation. The reasoning behind this approach is also dealt with in detail.

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A discrete method for the initialization of semi-discrete optimal transport problem

Lin

Guo

Xie

et al. 2021

Knowledge-Based Systems

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Evaluation of pairwise distances among orthogonal grid points in hypercube

Cited by 4 publications

References 4 publications

Formulation of Potential for Dynamical Particle System Applied to Monte Carlo Sampling

Formulation of Potential for Dynamical Particle System Applied to Monte Carlo Sampling

On the Influence of the Interaction Laws of a Dynamical Particle System for Sample Optimization

A discrete method for the initialization of semi-discrete optimal transport problem

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