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A novel hybrid sequential design strategy for global surrogate modeling of computer experiments

Karel Crombecq (UGent) , Dirk Gorissen (UGent) , Dirk Deschrijver (UGent) and Tom Dhaene (UGent)
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Abstract
Many complex real-world systems can be accurately modeled by simulations. However, high-fidelity simulations may take hours or even days to compute. Because this can be impractical, a surrogate model is often used to approximate the dynamic behavior of the original simulator. This model can then be used as a cheap, drop-in replacement for the simulator. Because simulations can be very expensive, the data points, which are required to build the model, must be chosen as optimally as possible. Sequential design strategies offer a huge advantage over one-shot experimental designs because they can use information gathered from previous data points in order to determine the location of new data points. Each sequential design strategy must perform a trade-off between exploration and exploitation, where the former involves selecting data points in unexplored regions of the design space, while the latter suggests adding data points in regions which were previously identified to be interesting (for example, highly nonlinear regions). In this paper, a novel hybrid sequential design strategy is proposed which uses a Monte Carlo-based approximation of a Voronoi tessellation for exploration and local linear approximations of the simulator for exploitation. The advantage of this method over other sequential design methods is that it is independent of the model type, and can therefore be used in heterogeneous modeling environments, where multiple model types are used at the same time. The new method is demonstrated on a number of test problems, showing that it is a robust, competitive, and efficient sequential design strategy.
Keywords
local linear approximation, active learning, experimental design, MICROWAVE CIRCUITS, nonlinear function approximation, RATIONAL INTERPOLATION MODELS, ENGINEERING DESIGN, sequential design, APPROXIMATION, MULTIVARIATE, POINTS, IBCN

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MLA
Crombecq, Karel, Dirk Gorissen, Dirk Deschrijver, et al. “A Novel Hybrid Sequential Design Strategy for Global Surrogate Modeling of Computer Experiments.” SIAM JOURNAL ON SCIENTIFIC COMPUTING 33.4 (2011): 1948–1974. Print.
APA
Crombecq, Karel, Gorissen, D., Deschrijver, D., & Dhaene, T. (2011). A novel hybrid sequential design strategy for global surrogate modeling of computer experiments. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 33(4), 1948–1974.
Chicago author-date
Crombecq, Karel, Dirk Gorissen, Dirk Deschrijver, and Tom Dhaene. 2011. “A Novel Hybrid Sequential Design Strategy for Global Surrogate Modeling of Computer Experiments.” Siam Journal on Scientific Computing 33 (4): 1948–1974.
Chicago author-date (all authors)
Crombecq, Karel, Dirk Gorissen, Dirk Deschrijver, and Tom Dhaene. 2011. “A Novel Hybrid Sequential Design Strategy for Global Surrogate Modeling of Computer Experiments.” Siam Journal on Scientific Computing 33 (4): 1948–1974.
Vancouver
1.
Crombecq K, Gorissen D, Deschrijver D, Dhaene T. A novel hybrid sequential design strategy for global surrogate modeling of computer experiments. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 2011;33(4):1948–74.
IEEE
[1]
K. Crombecq, D. Gorissen, D. Deschrijver, and T. Dhaene, “A novel hybrid sequential design strategy for global surrogate modeling of computer experiments,” SIAM JOURNAL ON SCIENTIFIC COMPUTING, vol. 33, no. 4, pp. 1948–1974, 2011.
@article{1936097,
  abstract     = {{Many complex real-world systems can be accurately modeled by simulations. However, high-fidelity simulations may take hours or even days to compute. Because this can be impractical, a surrogate model is often used to approximate the dynamic behavior of the original simulator. This model can then be used as a cheap, drop-in replacement for the simulator. Because simulations can be very expensive, the data points, which are required to build the model, must be chosen as optimally as possible. Sequential design strategies offer a huge advantage over one-shot experimental designs because they can use information gathered from previous data points in order to determine the location of new data points. Each sequential design strategy must perform a trade-off between exploration and exploitation, where the former involves selecting data points in unexplored regions of the design space, while the latter suggests adding data points in regions which were previously identified to be interesting (for example, highly nonlinear regions). In this paper, a novel hybrid sequential design strategy is proposed which uses a Monte Carlo-based approximation of a Voronoi tessellation for exploration and local linear approximations of the simulator for exploitation. The advantage of this method over other sequential design methods is that it is independent of the model type, and can therefore be used in heterogeneous modeling environments, where multiple model types are used at the same time. The new method is demonstrated on a number of test problems, showing that it is a robust, competitive, and efficient sequential design strategy.}},
  author       = {{Crombecq, Karel and Gorissen, Dirk and Deschrijver, Dirk and Dhaene, Tom}},
  issn         = {{1064-8275}},
  journal      = {{SIAM JOURNAL ON SCIENTIFIC COMPUTING}},
  keywords     = {{local linear approximation,active learning,experimental design,MICROWAVE CIRCUITS,nonlinear function approximation,RATIONAL INTERPOLATION MODELS,ENGINEERING DESIGN,sequential design,APPROXIMATION,MULTIVARIATE,POINTS,IBCN}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{1948--1974}},
  title        = {{A novel hybrid sequential design strategy for global surrogate modeling of computer experiments}},
  url          = {{http://dx.doi.org/10.1137/090761811}},
  volume       = {{33}},
  year         = {{2011}},
}

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