Dynamical model of repelling particles for construction of distance-based designs

Dynamical model of repelling particles for construction of distance-based designs

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A methodology is proposed for construction of uniformly distributed point sets within a design domain using an analogy to a dynamical system of interacting particles. It is shown that the distance-based fp criterion of optimality can be viewed as a potential energy of a system of charged particles. The potential energy is employed in derivation of the equations of motion of the particles. The dissipative dynamical system of mutually repelling particles can be simulated to achieve optimal and near-optimal arrangements of points (the design). The design domain is selected to be 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 fp criterion guarantees that the points are spread uniformly within the design domain. Periodicity assumption of the design domain is shown to be an elegant solution how to obtain statistically uniform coverage of the design domain. Solution to such an N-body system is presented. The designs obtained are shown to outperform the existing designs being optimized for multidimensional numerical integration.

A methodology is proposed for construction of uniformly distributed point sets within a design domain using an analogy to a dynamical system of interacting particles. It is shown that the distance-based fp criterion of optimality can be viewed as a potential energy of a system of charged particles. The potential energy is employed in derivation of the equations of motion of the particles. The dissipative dynamical system of mutually repelling particles can be simulated to achieve optimal and near-optimal arrangements of points (the design). The design domain is selected to be 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 fp criterion guarantees that the points are spread uniformly within the design domain. Periodicity assumption of the design domain is shown to be an elegant solution how to obtain statistically uniform coverage of the design domain. Solution to such an N-body system is presented. The designs obtained are shown to outperform the existing designs being optimized for multidimensional numerical integration.

phi criterion, Maximin criterion, Audze-Eglajs Uniform design, Low-discrepancy, Space-filling design, Design of Experiments, Monte Carlo Integration, Periodic space.

phi criterion, Maximin criterion, Audze-Eglajs Uniform design, Low-discrepancy, Space-filling design, Design of Experiments, Monte Carlo Integration, Periodic space.

VOŘECHOVSKÝ, M.; MAŠEK, J.; ELIÁŠ, J.

2020

22.09.2019

Hannover, Germany

978-981-11-2724-3

29th European safety and reliability conference (ESREL)

2663

2667

8

https://esrel2019.org/