IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v209y2021ics0951832021000016.html
   My bibliography  Save this article

B-splines on sparse grids for surrogates in uncertainty quantification

Author

Listed:
  • Rehme, Michael F.
  • Franzelin, Fabian
  • Pflüger, Dirk

Abstract

Robust prediction of the behavior of complex physical and engineering systems relies on approximating solutions in terms of physical and stochastic domains. For higher resolution and accuracy, simulation models must increase the number of deterministic and stochastic variables and therefore further increase the dimensionality of the problem. Sparse grids are an established technique to tackle higher-dimensional problems. Their efficient tensor product structure allows the creation of accurate surrogates from few model evaluations. Classical approaches use hat functions, resulting in non-differentiable surrogates, or global basis functions, resulting in potential instabilities. Therefore, we propose using modified not-a-knot B-splines to overcome both problems. Additionally, we use established spatially adaptive refinement criteria to reduce the number of model evaluations even further. We compare our technique to other data-driven uncertainty quantification methods in a real-world benchmark for probabilistic risk assessment for carbon dioxide storage in geological formations.

Suggested Citation

  • Rehme, Michael F. & Franzelin, Fabian & Pflüger, Dirk, 2021. "B-splines on sparse grids for surrogates in uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
  • Handle: RePEc:eee:reensy:v:209:y:2021:i:c:s0951832021000016
    DOI: 10.1016/j.ress.2021.107430
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832021000016
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ress.2021.107430?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. Hansson, Anders & Bryngelsson, Mårten, 2009. "Expert opinions on carbon dioxide capture and storage--A framing of uncertainties and possibilities," Energy Policy, Elsevier, vol. 37(6), pages 2273-2282, June.
    2. Oladyshkin, S. & Nowak, W., 2012. "Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 179-190.
    3. Du, Kai & Zhang, Qi, 2013. "Semi-linear degenerate backward stochastic partial differential equations and associated forward–backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1616-1637.
    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. Wang, Yangpeng & Li, Shuxiang & Lee, Kangkuen & Tam, Hwayaw & Qu, Yuanju & Huang, Jingyin & Chu, Xianghua, 2023. "Accident risk tensor-specific covariant model for railway accident risk assessment and prediction," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    2. Bansal, Parth & Zheng, Zhuoyuan & Shao, Chenhui & Li, Jingjing & Banu, Mihaela & Carlson, Blair E & Li, Yumeng, 2022. "Physics-informed machine learning assisted uncertainty quantification for the corrosion of dissimilar material joints," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    3. Kröker, Ilja & Oladyshkin, Sergey, 2022. "Arbitrary multi-resolution multi-wavelet-based polynomial chaos expansion for data-driven uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 222(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. Fujii, Masaaki & Takahashi, Akihiko, 2019. "Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1492-1532.
    2. Sun, Alexander Y., 2020. "Optimal carbon storage reservoir management through deep reinforcement learning," Applied Energy, Elsevier, vol. 278(C).
    3. Lee, Suh-Young & Lee, Jae-Uk & Lee, In-Beum & Han, Jeehoon, 2017. "Design under uncertainty of carbon capture and storage infrastructure considering cost, environmental impact, and preference on risk," Applied Energy, Elsevier, vol. 189(C), pages 725-738.
    4. Shang, Xiaobing & Su, Li & Fang, Hai & Zeng, Bowen & Zhang, Zhi, 2023. "An efficient multi-fidelity Kriging surrogate model-based method for global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    5. Krüger, Timmo, 2017. "Conflicts over carbon capture and storage in international climate governance," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 100(1), pages 58-67.
    6. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    7. Stephens, Jennie C. & Jiusto, Scott, 2010. "Assessing innovation in emerging energy technologies: Socio-technical dynamics of carbon capture and storage (CCS) and enhanced geothermal systems (EGS) in the USA," Energy Policy, Elsevier, vol. 38(4), pages 2020-2031, April.
    8. Zhang, Dongjie & Liu, Pei & Ma, Linwei & LI, Zheng, 2013. "A multi-period optimization model for planning of China's power sector with consideration of carbon dioxide mitigation—The importance of continuous and stable carbon mitigation policy," Energy Policy, Elsevier, vol. 58(C), pages 319-328.
    9. Zhai, Qingqing & Yang, Jun & Zhao, Yu, 2014. "Space-partition method for the variance-based sensitivity analysis: Optimal partition scheme and comparative study," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 66-82.
    10. de Cursi, Eduardo Souza, 2021. "Uncertainty quantification in game theory," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    11. Davies, Lincoln L. & Uchitel, Kirsten & Ruple, John, 2013. "Understanding barriers to commercial-scale carbon capture and sequestration in the United States: An empirical assessment," Energy Policy, Elsevier, vol. 59(C), pages 745-761.
    12. Zheng, Xiaohu & Yao, Wen & Zhang, Yunyang & Zhang, Xiaoya, 2022. "Consistency regularization-based deep polynomial chaos neural network method for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    13. Sébastien Chailleux, 2020. "Making the subsurface political: How enhanced oil recovery techniques reshaped the energy transition," Environment and Planning C, , vol. 38(4), pages 733-750, June.
    14. Iftikhar Ahmad & Ahsan Ayub & Uzair Ibrahim & Mansoor Khan Khattak & Manabu Kano, 2018. "Data-Based Sensing and Stochastic Analysis of Biodiesel Production Process," Energies, MDPI, vol. 12(1), pages 1-13, December.
    15. Shengwen Yin & Keliang Jin & Yu Bai & Wei Zhou & Zhonggang Wang, 2023. "Solution-Space-Reduction-Based Evidence Theory Method for Stiffness Evaluation of Air Springs with Epistemic Uncertainty," Mathematics, MDPI, vol. 11(5), pages 1-19, March.
    16. Yang, Xue & Zhang, Qi & Zhang, Tusheng, 2020. "Reflected backward stochastic partial differential equations in a convex domain," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6038-6063.
    17. Nils Markusson, 2012. "Born Again: The Debate on Lock-in and Ccs," Energy & Environment, , vol. 23(2-3), pages 389-394, May.
    18. Frankowska, Hélène & Zhang, Xu, 2020. "Necessary conditions for stochastic optimal control problems in infinite dimensions," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4081-4103.
    19. Rahman, Farahiyah Abdul & Aziz, Md Maniruzzaman A. & Saidur, R. & Bakar, Wan Azelee Wan Abu & Hainin, M.R & Putrajaya, Ramadhansyah & Hassan, Norhidayah Abdul, 2017. "Pollution to solution: Capture and sequestration of carbon dioxide (CO2) and its utilization as a renewable energy source for a sustainable future," Renewable and Sustainable Energy Reviews, Elsevier, vol. 71(C), pages 112-126.
    20. Koo, Jamin & Han, Kyusang & Yoon, En Sup, 2011. "Integration of CCS, emissions trading and volatilities of fuel prices into sustainable energy planning, and its robust optimization," Renewable and Sustainable Energy Reviews, Elsevier, vol. 15(1), pages 665-672, January.

    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:209:y:2021:i:c:s0951832021000016. 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.