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A fast active learning method in design of experiments: multipeak parallel adaptive infilling strategy based on expected improvement

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Abstract

Surrogate models are widely used in simulation-based engineering design. The distribution of samples directly determines the quality and efficiency of surrogate models, which has a significant influence on follow-up work. This paper proposes a multipeak parallel adaptive infilling (MPEI) strategy based on expected improvement (EI), which can be divided into two stages: the construction of candidate peak areas and the selection of appropriate candidates at the candidate peak areas. In the first stage, the candidates are divided into the corresponding subspaces in sequence according to the value of EI and the position of each candidate to construct the candidate peak areas. In the second stage, the Gaussian function is used to extract the uncorrelated parent point and the corresponding offspring points in each candidate peak area. Based on these stages, the MPEI strategy selects multiple new samples in spaces with both local optima and areas of large uncertainty interest, which can fully balance global exploration and local exploitation. In addition, the samples selected in each candidate peak area are concise and locally uniform, which can effectively reduce the computational cost. Seven benchmark cases and one engineering problem are used to validate the performance of the MPEI strategy. The results show that the MPEI strategy can efficiently obtain the desired prediction accuracy of surrogate models at a small price of a few samples and confirm the feasibility and robustness of the presented methodology.

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Funding

This research is financially supported by the National Key Research and Development Program of China (Grant No. 2018YFB1700704) and the National Natural Science Foundation of China (Grant No. 52075068).

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Authors and Affiliations

  1. School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China

    Yang Zhang, Shuo Wang, Chang’an Zhou & Xueguan Song

  2. Faculty of Mechanical Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou, 310016, China

    Liye Lv

Authors
  1. Yang Zhang
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  2. Shuo Wang
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  3. Chang’an Zhou
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  4. Liye Lv
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  5. Xueguan Song
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Correspondence to Xueguan Song.

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The main codes and raw data are submitted as supplementary materials.

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Responsible Editor: Xiaoping Du

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Appendix

Appendix

Table 10 The required AIIs when the performance of the surrogate model of BR case meets the specified requirements under different combinations of λ, Rp, and Rr
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Table 11 The required AIIs when the performance of the surrogate model of Camel3 case meets the specified requirements under different combinations of λ, Rp, and Rr
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Table 12 The required AINs when the performance of the surrogate model of BR case meets the specified requirements under different combinations of λ, Rp, and Rr
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Table 13 The required AINs when the performance of the surrogate model of Camel3 case meets the specified requirements under different combinations of λ, Rp, and Rr
Full size table

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Zhang, Y., Wang, S., Zhou, C. et al. A fast active learning method in design of experiments: multipeak parallel adaptive infilling strategy based on expected improvement. Struct Multidisc Optim 64, 1259–1284 (2021). https://doi.org/10.1007/s00158-021-02915-1

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  • DOI: https://doi.org/10.1007/s00158-021-02915-1

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