Publication detail

Distance-based optimal sampling in a hypercube: Analogies to N-body systems

VOŘECHOVSKÝ, M. MAŠEK, J. ELIÁŠ, J.

Original Title

Distance-based optimal sampling in a hypercube: Analogies to N-body systems

Type

journal article in Web of Science

Language

English

Original Abstract

A method is proposed for the construction of uniformly distributed point sets within a design domain using an analogy to a dynamical system of interacting particles. The possibility of viewing various distance-based optimality criteria as formulas representing the potential energy of a system of charged particles is discussed. The potential energy is employed in deriving the equations of motion of the particles. The particles are either attracted or repelled and dissipative dynamical systems can be simulated to achieve optimal and near-optimal arrangements of points. The design domain is set up as an Nvar-dimensional unit hypercube, with Nvar being the number of variables (factors). The number of points is equal to the number of simulations (levels). The periodicity assumption of the design domain is shown to be an elegant way to obtain statistically uniform coverage of the design domain. The ϕp criterion, which is a generalization of the Maximin criterion, is selected in order to demonstrate its analogy with an N-body system. This criterion guarantees that the points are spread uniformly within the design domain. The solution to such an N-body system is presented. The obtained designs are shown to outperform the existing optimal designs in various types of applications: multidimensional numerical integration, statistical exploration of computer models, reliability analyses of engineering systems, and screenings or exploratory designs for the global optimization/minimization of functions.

Keywords

criterion, Audze-Eglajs, Maximin criterion, MiniMax criterion, Periodic space, Space-filling design, Uniform design, Robust design, Low-discrepancy, Design of experiments, Latin hypercube sampling, Monte Carlo integration

Authors

VOŘECHOVSKÝ, M.; MAŠEK, J.; ELIÁŠ, J.

Released

10. 9. 2019

Publisher

Elsevier Science Ltd.

Location

Oxford, UK

ISBN

0965-9978

Periodical

ADVANCES IN ENGINEERING SOFTWARE

Year of study

137

Number

102709

State

United Kingdom of Great Britain and Northern Ireland

Pages from

1

Pages to

16

Pages count

16

URL

http://www.sciencedirect.com/science/article/pii/S0965997819301164

BibTex

@article{BUT159876,
  author="Miroslav {Vořechovský} and Jan {Mašek} and Jan {Eliáš}",
  title="Distance-based optimal sampling in a hypercube: Analogies to N-body systems",
  journal="ADVANCES IN ENGINEERING SOFTWARE",
  year="2019",
  volume="137",
  number="102709",
  pages="1--16",
  doi="10.1016/j.advengsoft.2019.102709",
  issn="0965-9978",
  url="http://www.sciencedirect.com/science/article/pii/S0965997819301164"
}