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Minimum Potential Energy Designs

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

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  1. Minimum Potential Energy Designs Bradley Jones & Christopher Gotwalt SAS Institute Inc.

  2. 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

  3. Illustration of Core Idea

  4. Objective function where dij is the distance between the ith and jth points. Goal: Find the design that minimizes the above function

  5. Spherical Symmetry – Uniform Spacing

  6. Near Orthogonal 12 Factor 24 Run Design

  7. Estimation Efficiency for Low Order Polynomial Models D-Efficiency for full quadratic model. Four and five factor designs have an added center point.

  8. Two Factor Designs

  9. 4 points

  10. 5 points

  11. 6 points

  12. 7 points

  13. 8 points

  14. 9 points

  15. 10 points

  16. 11 points

  17. 12 points

  18. 13 points

  19. 14 points

  20. 15 points

  21. 16 Points

  22. 17 Points

  23. 18 Points

  24. 19 Points

  25. 20 Points

  26. 50 points

  27. 96 Points

  28. 200 Points

  29. Three Factors

  30. Four Factors

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

  32. Contact Information Bradley.Jones@jmp.com

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