Hierarchical Multi-fidelity Surrogate Modeling

  • Chapter
  • First Online:
Multi-fidelity Surrogates

Part of the book series: Engineering Applications of Computational Methods ((EACM,volume 12))

  • 405 Accesses

Abstract

Most of the existing multi-fidelity (MF) surrogates assume that high-fidelity (HF) models are generally more accurate than low-fidelity (LF) models but LF models are less expensive than HF models. In other words, the fidelity levels between the HF and LF models can be clearly identified, which is the core concept of hierarchical multi-fidelity surrogate modeling. The motivation of MF surrogate modeling is that a large number of inexpensive LF sampling points can be used to decrease the computational cost, while a limited number of expensive HF sampling points can be used to ensure the prediction accuracy of the surrogate model.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 139.09
Price includes VAT (Germany)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 181.89
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
EUR 181.89
Price includes VAT (Germany)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Chang KJ, Haftka RT, Giles GL, Kao IJ (1993) Sensitivity-based scaling for approximating structural response. J Aircr 30:283–288

    Article  Google Scholar 

  2. Gano SE, Renaud JE, Martin JD, Simpson TW (2006) Update strategies for kriging models used in variable fidelity optimization. Struct Multidiscip Optim 32:287–298

    Article  Google Scholar 

  3. **ong Y, Chen W, Tsui K-L (2008) A new variable-fidelity optimization framework based on model fusion and objective-oriented sequential sampling. J Mech Des 130:111401–111409

    Article  Google Scholar 

  4. Han Z-H, Görtz S, Zimmermann R (2013) Improving variable-fidelity surrogate modeling via gradient-enhanced kriging and a generalized hybrid bridge function. Aerosp Sci Technol 25:177–189

    Article  Google Scholar 

  5. Tyan M, Nguyen NV, Lee J-W (2014) Improving variable-fidelity modelling by exploring global design space and radial basis function networks for aerofoil design. Eng Optim 47:885–908

    Article  Google Scholar 

  6. Song X, Lv L, Sun W, Zhang J (2019) A radial basis function-based multi-fidelity surrogate model: exploring correlation between high-fidelity and low-fidelity models 1–17

    Google Scholar 

  7. Shu L, Jiang P, Song X, Zhou Q (2019) Novel approach for selecting low-fidelity scale factor in multifidelity metamodeling. AIAA J 1–11

    Google Scholar 

  8. Zhou Q, Wu J, Xue T, ** P (2019) A two-stage adaptive multi-fidelity surrogate model-assisted multi-objective genetic algorithm for computationally expensive problems. Eng Comput 1–17.

    Google Scholar 

  9. Liu Y, Collette M (2014) Improving surrogate-assisted variable fidelity multi-objective optimization using a clustering algorithm. Appl Soft Comput 24:482–493

    Article  Google Scholar 

  10. Li X, Qiu H, Jiang Z, Gao L, Shao X (2017) A VF-SLP framework using least squares hybrid scaling for RBDO. Struct Multidiscip Optim 55:1629–1640

    Article  MathSciNet  Google Scholar 

  11. Gano SE, Renaud JE, Sanders B (2005) Hybrid variable fidelity optimization by using a kriging-based scaling function. AIAA J 43:2422–2433

    Article  Google Scholar 

  12. Rayas-Sanchez JE (2016) Power in simplicity with ASM: tracing the aggressive space map** algorithm over two decades of development and engineering applications. IEEE Microwave Mag 17:64–76

    Article  Google Scholar 

  13. Wang H, Fan T, Li G (2017) Reanalysis-based space map** method, an alternative optimization way for expensive simulation-based problems. Struct Multidiscip Optim 55:2143–2157

    Article  Google Scholar 

  14. Robinson T, Eldred M, Willcox K, Haimes R (2008) Surrogate-based optimization using multifidelity models with variable parameterization and corrected space map**. AIAA J 46:2814–2822

    Article  Google Scholar 

  15. Journel AG, Huijbregts CJ (1978) Mining geostatistics. Academic Press, London

    Google Scholar 

  16. Hastie TJ, Tibshirani RJ, Friedman JH (2001) The elements of statistical learning. Elements 1

    Google Scholar 

  17. Gano S, Sanders B, Renaud J (2004) Variable fidelity optimization using a kriging based scaling function. In: 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, p 4460

    Google Scholar 

  18. **ong Y, Chen W, Tsui K-L (2007) A new variable fidelity optimization framework based on model fusion and objective-oriented sequential sampling. In: International design engineering technical conferences and computers and information in engineering conference, pp 699–708

    Google Scholar 

  19. Zheng J, Shao X, Gao L, Jiang P, Qiu H (2014) A prior-knowledge input LSSVR metamodeling method with tuning based on cellular particle swarm optimization for engineering design. Expert Syst Appl 41:2111–2125

    Article  Google Scholar 

  20. Acar E (2010) Various approaches for constructing an ensemble of metamodels using local measures. Struct Multidiscip Optim 42:879–896

    Article  Google Scholar 

  21. **ao JZ, Ma YZ, Xu FL (2011) Ensemble of surrogates with recursive arithmetic average. Struct Multidiscip Optim 44

    Google Scholar 

  22. Park J-S (1994) Optimal Latin-hypercube designs for computer experiments. J Stat Plann Infer 39:95–111

    Article  MathSciNet  MATH  Google Scholar 

  23. Zadeh PM, Toropov VV, Wood AS (2009) Metamodel-based collaborative optimization framework. Struct Multidiscip Optim 38:103–115

    Article  Google Scholar 

  24. Gao L, **ao M, Shao X, Jiang P, Nie L, Qiu H (2012) Analysis of gene expression programming for approximation in engineering design. Struct Multidiscip Optim 46:399–413

    Article  Google Scholar 

  25. Zheng J, Shao X, Gao L, Jiang P, Li Z (2013) A hybrid variable-fidelity global approximation modelling method combining tuned radial basis function base and kriging correction. J Eng Des 24:604–622

    Article  Google Scholar 

  26. Park C, Haftka RT, Kim NH (2017) Remarks on multi-fidelity surrogates. Struct Multidiscip Optim 55:1029–1050

    Article  MathSciNet  Google Scholar 

  27. Park C, Haftka RT, Kim NH (2018) Low-fidelity scale factor improves Bayesian multi-fidelity prediction by reducing bumpiness of discrepancy function. Struct Multidiscip Optim

    Google Scholar 

  28. Ben Salem M, Tomaso L (2018) Automatic selection for general surrogate models. Struct Multidiscip Optim

    Google Scholar 

  29. Cressie N (1992) Statistics for spatial data. Terra Nova 4:613–617

    Article  Google Scholar 

  30. Wang GG (2003) Adaptive response surface method using inherited latin hypercube design points. J Mech Des 125:210–220

    Article  Google Scholar 

  31. Shu L, Jiang P, Zhou Q, Shao X, Hu J, Meng X (2018) An on-line variable fidelity metamodel assisted multi-objective genetic algorithm for engineering design optimization. Appl Soft Comput 66:438–448

    Article  Google Scholar 

  32. Han Z-H, Görtz S (2012) Hierarchical kriging model for variable-fidelity surrogate modeling. AIAA J 50:1885–1896

    Article  Google Scholar 

  33. Shu L, Jiang P, Wan L, Zhou Q, Shao X, Zhang Y (2017) Metamodel-based design optimization employing a novel sequential sampling strategy. Eng Comput 34:2547–2564

    Article  Google Scholar 

  34. Zhou Q, Wang Y, Choi S-K, Jiang P, Shao X, Hu J (2017) A sequential multi-fidelity metamodeling approach for data regression. Knowl-Based Syst 134:199–212

    Article  Google Scholar 

  35. Zhou Q, Shao X, Jiang P, Gao Z, Wang C, Shu L (2016) An active learning metamodeling approach by sequentially exploiting difference information from variable-fidelity models. Adv Eng Inform 30:283–297

    Article  Google Scholar 

  36. Lim D, Ong Y-S, ** Y, Sendhoff B (2007) A study on metamodeling techniques, ensembles, and multi-surrogates in evolutionary computation. In: Proceedings of the 9th annual conference on genetic and evolutionary computation, ACM, pp 1288–1295

    Google Scholar 

  37. Kleijnen JPC (2017) Regression and Kriging metamodels with their experimental designs in simulation: a review. Eur J Oper Res 256:1–16

    Article  MathSciNet  MATH  Google Scholar 

  38. Lophaven SN, Nielsen HB, Søndergaard J (2002) Aspects of the matlab toolbox DACE. In: Informatics and mathematical modelling. Technical University of Denmark, DTU

    Google Scholar 

  39. Xu S, Liu H, Wang X, Jiang X (2014) A robust error-pursuing sequential sampling approach for global metamodeling based on voronoi diagram and cross validation. J Mech Des 136:071009

    Article  Google Scholar 

  40. Kleijnen JPC (2009) Kriging metamodeling in simulation: a review. Eur J Oper Res 192:707–716

    Article  MathSciNet  MATH  Google Scholar 

  41. Zhou X, Jiang T (2016) Metamodel selection based on stepwise regression. Struct Multidiscip Optim 1–17

    Google Scholar 

  42. Aute V, Saleh K, Abdelaziz O, Azarm S, Radermacher R (2013) Cross-validation based single response adaptive design of experiments for Kriging metamodeling of deterministic computer simulations. Struct Multidiscip Optim 48:581–605

    Article  Google Scholar 

  43. **ao M, Gao L, Shao X, Qiu H, Jiang P (2012) A generalised collaborative optimisation method and its combination with kriging metamodels for engineering design. J Eng Des 23:379–399

    Article  Google Scholar 

  44. Zhao D, Xue D (2010) A comparative study of metamodeling methods considering sample quality merits. Struct Multidiscip Optim 42:923–938

    Article  Google Scholar 

  45. Zhou Q, Shao X, Jiang P, Zhou H, Shu L (2015) An adaptive global variable fidelity metamodeling strategy using a support vector regression based scaling function. Simul Model Pract Theor 59:18–35

    Google Scholar 

  46. ** R, Chen W, Sudjianto A (2005) An efficient algorithm for constructing optimal design of computer experiments. J Stat Plann Infer 134:268–287

    Article  MathSciNet  MATH  Google Scholar 

  47. Qiu H, Xu Y, Gao L, Li X, Chi L (2016) Multi-stage design space reduction and metamodeling optimization method based on self-organizing maps and fuzzy clustering. Expert Syst Appl 46:180–195

    Article  Google Scholar 

  48. Lophaven SN, Nielsen HB, Søndergaard J (2002) DACE: a Matlab kriging toolbox, Citeseer

    Google Scholar 

  49. Martin JD, Simpson TWJAJ (2005) Use of kriging models to approximate deterministic computer models 43:853–863

    Google Scholar 

  50. Warnes J, Ripley BJB (1987) Problems with likelihood estimation of covariance functions of spatial Gaussian processes 74:640–642

    Google Scholar 

  51. Mardia K, Watkins AJB (1989) On multimodality of the likelihood in the spatial linear model 76:289–295

    Google Scholar 

  52. Homaifar A, Qi CX, Lai SH (1994) Constrained optimization via genetic algorithms. Simulation 62:242–253

    Article  Google Scholar 

  53. Shu LS, Jiang P, Zhou Q, **e TL (2019) An online variable-fidelity optimization approach for multi-objective design optimization. Struct Multidiscip Optim 60:1059–1077

    Article  MathSciNet  Google Scholar 

  54. Han Z, Xu C, Zhang L, Zhang Y, Zhang K, Song W (2019) Efficient aerodynamic shape optimization using variable-fidelity surrogate models and multilevel computational grids. Chin J Aeronaut 1–19

    Google Scholar 

  55. Zhou Q, Wang Y, Choi S-K, Jiang P, Shao X, Hu J, Shu L (2018) A robust optimization approach based on multi-fidelity metamodel. Struct Multidiscip Optim 57:775–797

    Article  Google Scholar 

  56. Kennedy MC, O’Hagan A (2000) Predicting the output from a complex computer code when fast approximations are available. Biometrika 87:1–13

    Article  MathSciNet  MATH  Google Scholar 

  57. Liu Y, Chen S, Wang F, **ong FJS, Optimization M (2018) Sequential optimization using multi-level cokriging and extended expected improvement criterion 58:1155–1173

    Google Scholar 

  58. Forrester AI, Sóbester A, Keane AJ (2007) Multi-fidelity optimization via surrogate modelling. In: Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences. The Royal Society, pp 3251–3269

    Google Scholar 

  59. **ong S, Qian PZG, Wu CFJ (2013) Sequential design and analysis of high-accuracy and low-accuracy computer codes. Technometrics 55:37–46

    Article  MathSciNet  Google Scholar 

  60. Toal DJ (2015) Some considerations regarding the use of multi-fidelity Kriging in the construction of surrogate models. Struct Multidiscip Optim 51:1223–1245

    Article  Google Scholar 

  61. Helton JC, Davis FJ (2003) Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab Eng Syst Saf 81:23–69

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qi Zhou .

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zhou, Q., Zhao, M., Hu, J., Ma, M. (2023). Hierarchical Multi-fidelity Surrogate Modeling. In: Multi-fidelity Surrogates. Engineering Applications of Computational Methods, vol 12. Springer, Singapore. https://doi.org/10.1007/978-981-19-7210-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-981-19-7210-2_2

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-7209-6

  • Online ISBN: 978-981-19-7210-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Navigation