Overview of Surrogate papers at WCSMO7

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Overview of Surrogate papers at WCSMO7
S. Sakata (Shimane University) R.T. Haftka
(University of Florida)

• Surrogate application papers
• What problems call for surrogate use?
• What surrogates are popular?
• Improvement in surrogates
• Multiple surrogates, combined surrogates,
  combining multiple fidelity models, improving
  accuracy, obtaining better error estimates,
  reducing dimensionality
• Some of papers cannot be classified into these
  categories, but those should be also encouraged
  to be developed.

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What problems call for surrogates?

• Surrogates are particularly useful when the
  number of times they are used is large compared
  to the number of simulations needed to construct
  them
• Global optimization, multiobjective optimization
  and Monte Carlo simulations require large number
  of calls to surrogate

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Application problems

• Genetic algorithms
• Salajegheh et al.,F-L Lee et al., J Lee and
  Jeong, Kalmar et al.,
• Other global optimization
• Markine et al., Chang and Chen,
• Local optimization
• Samad et al. or several others
• Reliability
• Jeon et al, K-H Lee et al.

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Type of surrogates used

• The growing speed of computers is mostly used for
  conducting more complex simulations rather than
  for running simulations faster
• Therefore, for a given surrogate, the cost of
  constructing compared to cost of simulations
  becomes small over time
• Consequently we see movement from cheap to more
  expensive surrogates
• Linear regression requires only solution of
  algebraic equations
• Kriging, Neural networks, support vector
  regression require optimization
• Simultaneous multiple surrogates require multiple
  optimizations

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Surrogates used

• Polynomial RSM
• Zhang et al., Yang et al., K-H Lee et al, Jeon et
  al.,, Kang et al., Gogu et al., Chang et al., .
• MARS Markine et al.
• Kriging
• Byun et al., Sakata et al., Auzins et al.,Xiong
  et al. Han et al.,Park et al., C.Choi et al.,
  J.J. Jung. ,.
• Neural networks (including RBF)
• Salajegheh et al., F-L Lee et al.,Golestanian et
  al., J. Lee et al., Sun et al. Gustafsson et
  al., Kitayama et al., Kucerova et al., Bailey.
• Multiple surrogate
• Samad et al., Goel et al.

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Improvements in surrogates

• Multiple optimization based on multiple
  surrogates Samad et al.
• Fusing multi-fidelity model Xiong and Chen
• Combining Kriging with quadratic RSM Sakata and
  Ashida
• Reliability-based approach C. Kim and K.K. Choi
• Design space transformation with stretching
  functions Jeon et al.
• Higher order RSMs Chang and Chen
• Enhancing feasibility J. Lee et al.
• Techniques for reducing number of variables Gogu
  et al.
• Accurate error estimators Goel et al., Byun et
  al.,
• Library of Approximations Gresovnik and Rodic

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Possible future challenges

• Multiple cycles and theory
• In most applications a single surrogate is
  constructed
• In some a first surrogate is used to zoom on
  region of interest
• How do we know when to stop? Especially when we
  seek global optimum
• Number of variables
• Can we go beyond 30-50 variables?
• Multiple fidelity evaluations
• How do we select the optimal level of fidelity at
  different points of the design of experiments?

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Possible future challenges

• And also continue to try to solve problems as
• How to construct a better surrogate.
• How to construct a surrogate stably, cheap,
  without expert.
• How to select a samples in using the flexible
  methods or a large numbers of variables.