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Minimum Potential Energy Designs. Bradley Jones & Christopher Gotwalt SAS Institute Inc. Abstract. Introducing a new class of space filling designs based on a physical analogy of design points as protons connected by springs. Properties Spherical symmetry Nearly orthogonal

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minimum potential energy designs
Minimum Potential Energy Designs

Bradley Jones

&

Christopher Gotwalt

SAS Institute Inc.

abstract
Abstract
  • Introducing a new class of space filling designs based on a physical analogy of design points as protons connected by springs.
  • Properties
    • Spherical symmetry
    • Nearly orthogonal
    • Uniform Spacing
    • Easy to compute with unconstrained optimization code
  • Outline
    • Show how to generate these designs
    • Discuss their properties
    • Give examples with different numbers of factors & sample sizes
objective function
Objective function

where dij is the distance between the ith and jth points.

Goal: Find the design that minimizes the above function

near orthogonal
Near Orthogonal

12 Factor 24 Run Design

estimation efficiency for low order polynomial models
Estimation Efficiency for Low Order Polynomial Models

D-Efficiency for full quadratic model.

Four and five factor designs have an added center point.

conclusions
Conclusions
  • Benefits
    • Spherical symmetry
    • Nearly orthogonal
    • Uniform Spacing
    • Available in commercial software
  • Negative
    • Not “space filling” in higher dimensions (except in low dimensional projections.
contact information
Contact Information

Bradley.Jones@jmp.com