IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v247y2024ics0951832024001947.html
   My bibliography  Save this article

Probabilistic surrogate modeling by Gaussian process: A new estimation algorithm for more robust prediction

Author

Listed:
  • Marrel, Amandine
  • Iooss, Bertrand

Abstract

In reliability engineering studies, computer codes are increasingly used to model physical phenomena which, in many cases, can be very time-consuming to run. A widely accepted approach consists in approximating the CPU-time expensive computer model by a surrogate model. One of the most popular surrogate model is the Gaussian Process regression, as it provides, additionally to a prediction at an unobserved point, an uncertainty around this prediction (a predictive distribution). However, in practice, the quality of this metamodel depends on several choices, as the estimation and validation algorithms. The present work aims at proposing a new algorithm, based on constrained optimization multi-objective techniques, to estimate the Gaussian process hyperparameters in order to ensure robust and accurate (i.e. reliable) predictive distribution of the Gaussian process. An intensive numerical benchmark on various analytical functions, with different input dimensions and learning sample sizes, shows its good performance in comparison with standard estimation algorithms. The new algorithm is also applied to a real test case modeling an aquatic ecosystem. It is compared with a recent robust and sophisticated Bayesian method; it proves to be as efficient while being less sensitive to the specification of the Gaussian process model.

Suggested Citation

  • Marrel, Amandine & Iooss, Bertrand, 2024. "Probabilistic surrogate modeling by Gaussian process: A new estimation algorithm for more robust prediction," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
  • Handle: RePEc:eee:reensy:v:247:y:2024:i:c:s0951832024001947
    DOI: 10.1016/j.ress.2024.110120
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832024001947
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ress.2024.110120?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marrel, Amandine & Iooss, Bertrand, 2024. "Probabilistic surrogate modeling by Gaussian process: A review on recent insights in estimation and validation," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    2. Ma, Yuan-Zhuo & Jin, Xiang-Xiang & Wu, Xi-Long & Xu, Chang & Li, Hong-Shuang & Zhao, Zhen-Zhou, 2023. "Reliability-based design optimization using adaptive Kriging-A single-loop strategy and a double-loop one," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    3. Betancourt, José & Bachoc, François & Klein, Thierry & Idier, Déborah & Pedreros, Rodrigo & Rohmer, Jérémy, 2020. "Gaussian process metamodeling of functional-input code for coastal flood hazard assessment," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    4. Lee W. Schruben, 1980. "A Coverage Function for Interval Estimators of Simulation Response," Management Science, INFORMS, vol. 26(1), pages 18-27, January.
    5. Perrin, G., 2020. "Adaptive calibration of a computer code with time-series output," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    6. Becker, William, 2020. "Metafunctions for benchmarking in sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    7. Bachoc, François, 2013. "Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 55-69.
    8. Ribaud, Mélina & Blanchet-Scalliet, Christophette & Helbert, Céline & Gillot, Frédéric, 2020. "Robust optimization: A kriging-based multi-objective optimization approach," Reliability Engineering and System Safety, Elsevier, vol. 200(C).
    9. Huang, Shi-Ya & Zhang, Shao-He & Liu, Lei-Lei, 2022. "A new active learning Kriging metamodel for structural system reliability analysis with multiple failure modes," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    10. Iooss, Bertrand & Le Gratiet, Loïc, 2019. "Uncertainty and sensitivity analysis of functional risk curves based on Gaussian processes," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 58-66.
    11. Acharki, Naoufal & Bertoncello, Antoine & Garnier, Josselin, 2023. "Robust prediction interval estimation for Gaussian processes by cross-validation method," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    12. Robert Thorndike, 1953. "Who belongs in the family?," Psychometrika, Springer;The Psychometric Society, vol. 18(4), pages 267-276, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marrel, Amandine & Iooss, Bertrand, 2024. "Probabilistic surrogate modeling by Gaussian process: A review on recent insights in estimation and validation," Reliability Engineering and System Safety, Elsevier, vol. 247(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marrel, Amandine & Iooss, Bertrand, 2024. "Probabilistic surrogate modeling by Gaussian process: A review on recent insights in estimation and validation," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    2. Nan, Hang & Liang, Hao & Di, Haoyuan & Li, Hongshuang, 2024. "A gradient-assisted learning strategy of Kriging model for robust design optimization," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    3. Li, Bingyi & Jia, Xiang & Long, Jiahui, 2024. "AK–TSAGL: A two-stage hybrid algorithm combining global exploration and local exploitation based on active learning for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 250(C).
    4. Koecklin, Manuel Tong & Longoria, Genaro & Fitiwi, Desta Z. & DeCarolis, Joseph F. & Curtis, John, 2021. "Public acceptance of renewable electricity generation and transmission network developments: Insights from Ireland," Energy Policy, Elsevier, vol. 151(C).
    5. Acharki, Naoufal & Bertoncello, Antoine & Garnier, Josselin, 2023. "Robust prediction interval estimation for Gaussian processes by cross-validation method," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    6. Becken, Susanne & Stantic, Bela & Chen, Jinyan & Connolly, Rod M., 2022. "Twitter conversations reveal issue salience of aviation in the broader context of climate change," Journal of Air Transport Management, Elsevier, vol. 98(C).
    7. Orietta Nicolis & Jean Paul Maidana & Fabian Contreras & Danilo Leal, 2024. "Analyzing the Impact of COVID-19 on Economic Sustainability: A Clustering Approach," Sustainability, MDPI, vol. 16(4), pages 1-30, February.
    8. Rockstuhl, Sebastian & Wenninger, Simon & Wiethe, Christian & Ahlrichs, Jakob, 2022. "The influence of risk perception on energy efficiency investments: Evidence from a German survey," Energy Policy, Elsevier, vol. 167(C).
    9. Tong Koecklin, Manuel & Fitiwi, Desta & de Carolis, Joseph F. & Curtis, John, 2020. "Renewable electricity generation and transmission network developments in light of public opposition: Insights from Ireland," Papers WP653, Economic and Social Research Institute (ESRI).
    10. Archana R. Panhalkar & Dharmpal D. Doye, 2020. "An approach of improving decision tree classifier using condensed informative data," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 47(4), pages 431-445, December.
    11. Michele Cincera, 2005. "Firms' productivity growth and R&D spillovers: An analysis of alternative technological proximity measures," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 14(8), pages 657-682.
    12. Horstmann, Felix, 2017. "Measuring the shopper's attitude toward the point of sale display: Scale development and validation," Journal of Retailing and Consumer Services, Elsevier, vol. 36(C), pages 112-123.
    13. Junyong Jang & Yongbin Cho & Juntae Park, 2024. "Bus Route Sketching: A Multimetric Analysis from the User’s and Operator’s Perspectives," Sustainability, MDPI, vol. 16(16), pages 1-19, August.
    14. Elizaveta Zinovyeva & Raphael C. G. Reule & Wolfgang Karl Hardle, 2021. "Understanding Smart Contracts: Hype or Hope?," Papers 2103.08447, arXiv.org.
    15. Jiang, Xia & Lu, Zhenzhou, 2024. "A novel quantile-based sequential optimization and reliability assessment method for safety life analysis," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    16. Torii, André Jacomel & Novotny, Antonio André, 2021. "A priori error estimates for local reliability-based sensitivity analysis with Monte Carlo Simulation," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    17. Zhao, Yingrui & Hu, Songhua & Zhang, Ming, 2024. "Evaluating equitable Transit-Oriented development (TOD) via the Node-Place-People model," Transportation Research Part A: Policy and Practice, Elsevier, vol. 185(C).
    18. Dario Cottafava & Giulia Sonetti & Paolo Gambino & Andrea Tartaglino, 2018. "Explorative Multidimensional Analysis for Energy Efficiency: DataViz versus Clustering Algorithms," Energies, MDPI, vol. 11(5), pages 1-18, May.
    19. Rivier, M. & Congedo, P.M., 2022. "Surrogate-Assisted Bounding-Box approach applied to constrained multi-objective optimisation under uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    20. López-Lopera, Andrés F. & Idier, Déborah & Rohmer, Jérémy & Bachoc, François, 2022. "Multioutput Gaussian processes with functional data: A study on coastal flood hazard assessment," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:247:y:2024:i:c:s0951832024001947. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.