IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v15y2022i20p7697-d946195.html
   My bibliography  Save this article

Physics-Informed Neural Network Solution of Point Kinetics Equations for a Nuclear Reactor Digital Twin

Author

Listed:
  • Konstantinos Prantikos

    (School of Nuclear Engineering, Purdue University, West Lafayette, IN 47906, USA
    Nuclear Science and Engineering Division, Argonne National Laboratory, Argonne, IL 60439, USA)

  • Lefteri H. Tsoukalas

    (School of Nuclear Engineering, Purdue University, West Lafayette, IN 47906, USA)

  • Alexander Heifetz

    (Nuclear Science and Engineering Division, Argonne National Laboratory, Argonne, IL 60439, USA)

Abstract

A digital twin (DT) for nuclear reactor monitoring can be implemented using either a differential equations-based physics model or a data-driven machine learning model. The challenge of a physics-model-based DT consists of achieving sufficient model fidelity to represent a complex experimental system, whereas the challenge of a data-driven DT consists of extensive training requirements and a potential lack of predictive ability. We investigate the performance of a hybrid approach, which is based on physics-informed neural networks (PINNs) that encode fundamental physical laws into the loss function of the neural network. We develop a PINN model to solve the point kinetic equations (PKEs), which are time-dependent, stiff, nonlinear, ordinary differential equations that constitute a nuclear reactor reduced-order model under the approximation of ignoring spatial dependence of the neutron flux. The PINN model solution of PKEs is developed to monitor the start-up transient of Purdue University Reactor Number One (PUR-1) using experimental parameters for the reactivity feedback schedule and the neutron source. The results demonstrate strong agreement between the PINN solution and finite difference numerical solution of PKEs. We investigate PINNs performance in both data interpolation and extrapolation. For the test cases considered, the extrapolation errors are comparable to those of interpolation predictions. Extrapolation accuracy decreases with increasing time interval.

Suggested Citation

  • Konstantinos Prantikos & Lefteri H. Tsoukalas & Alexander Heifetz, 2022. "Physics-Informed Neural Network Solution of Point Kinetics Equations for a Nuclear Reactor Digital Twin," Energies, MDPI, vol. 15(20), pages 1-22, October.
  • Handle: RePEc:gam:jeners:v:15:y:2022:i:20:p:7697-:d:946195
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/15/20/7697/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/1996-1073/15/20/7697/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Changhyun Kim & Minh-Chau Dinh & Hae-Jin Sung & Kyong-Hwan Kim & Jeong-Ho Choi & Lukas Graber & In-Keun Yu & Minwon Park, 2022. "Design, Implementation, and Evaluation of an Output Prediction Model of the 10 MW Floating Offshore Wind Turbine for a Digital Twin," Energies, MDPI, vol. 15(17), pages 1-16, August.
    2. Brendan Kochunas & Xun Huan, 2021. "Digital Twin Concepts with Uncertainty for Nuclear Power Applications," Energies, MDPI, vol. 14(14), pages 1-32, July.
    3. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
    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. Harleen Kaur Sandhu & Saran Srikanth Bodda & Abhinav Gupta, 2023. "A Future with Machine Learning: Review of Condition Assessment of Structures and Mechanical Systems in Nuclear Facilities," Energies, MDPI, vol. 16(6), pages 1-23, March.
    2. Alexandra Akins & Derek Kultgen & Alexander Heifetz, 2023. "Anomaly Detection in Liquid Sodium Cold Trap Operation with Multisensory Data Fusion Using Long Short-Term Memory Autoencoder," Energies, MDPI, vol. 16(13), pages 1-19, June.

    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. Kristina O. F. Williams & Benjamin F. Akers, 2023. "Numerical Simulation of the Korteweg–de Vries Equation with Machine Learning," Mathematics, MDPI, vol. 11(13), pages 1-14, June.
    2. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Working Papers hal-03145949, HAL.
    3. Zhouzhou Gu & Mathieu Lauri`ere & Sebastian Merkel & Jonathan Payne, 2024. "Global Solutions to Master Equations for Continuous Time Heterogeneous Agent Macroeconomic Models," Papers 2406.13726, arXiv.org.
    4. Raval, Khushi Jatinkumar & Jadav, Nilesh Kumar & Rathod, Tejal & Tanwar, Sudeep & Vimal, Vrince & Yamsani, Nagendar, 2024. "A survey on safeguarding critical infrastructures: Attacks, AI security, and future directions," International Journal of Critical Infrastructure Protection, Elsevier, vol. 44(C).
    5. Parand, K. & Aghaei, A.A. & Jani, M. & Ghodsi, A., 2021. "A new approach to the numerical solution of Fredholm integral equations using least squares-support vector regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 114-128.
    6. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Papers 2102.09851, arXiv.org, revised Feb 2021.
    7. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2022. "Deep Stochastic Optimization in Finance," Papers 2205.04604, arXiv.org.
    8. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
    9. Shuaiqiang Liu & Cornelis W. Oosterlee & Sander M. Bohte, 2019. "Pricing Options and Computing Implied Volatilities using Neural Networks," Risks, MDPI, vol. 7(1), pages 1-22, February.
    10. Bastien Baldacci & Joffrey Derchu & Iuliia Manziuk, 2020. "An approximate solution for options market-making in high dimension," Papers 2009.00907, arXiv.org.
    11. Alexandre Pannier & Cristopher Salvi, 2024. "A path-dependent PDE solver based on signature kernels," Papers 2403.11738, arXiv.org, revised Oct 2024.
    12. Lv, Zhihan & Cheng, Chen & Lv, Haibin, 2023. "Digital twins for secure thermal energy storage in building," Applied Energy, Elsevier, vol. 338(C).
    13. Rong Du & Duy-Minh Dang, 2023. "Fourier Neural Network Approximation of Transition Densities in Finance," Papers 2309.03966, arXiv.org, revised Sep 2024.
    14. Ali Al-Aradi & Adolfo Correia & Danilo de Frietas Naiff & Gabriel Jardim & Yuri Saporito, 2019. "Extensions of the Deep Galerkin Method," Papers 1912.01455, arXiv.org, revised Apr 2022.
    15. Yuga Iguchi & Riu Naito & Yusuke Okano & Akihiko Takahashi & Toshihiro Yamada, 2021. "Deep Asymptotic Expansion: Application to Financial Mathematics," CIRJE F-Series CIRJE-F-1178, CIRJE, Faculty of Economics, University of Tokyo.
    16. Martin Hutzenthaler & Arnulf Jentzen & Thomas Kruse & Tuan Anh Nguyen, 2020. "A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations," Partial Differential Equations and Applications, Springer, vol. 1(2), pages 1-34, April.
    17. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen, 2020. "Pricing and Hedging American-Style Options with Deep Learning," JRFM, MDPI, vol. 13(7), pages 1-12, July.
    18. Salah A. Faroughi & Ramin Soltanmohammadi & Pingki Datta & Seyed Kourosh Mahjour & Shirko Faroughi, 2023. "Physics-Informed Neural Networks with Periodic Activation Functions for Solute Transport in Heterogeneous Porous Media," Mathematics, MDPI, vol. 12(1), pages 1-23, December.
    19. Jiequn Han & Ruimeng Hu & Jihao Long, 2020. "Convergence of Deep Fictitious Play for Stochastic Differential Games," Papers 2008.05519, arXiv.org, revised Mar 2021.
    20. Zio, Enrico & Miqueles, Leonardo, 2024. "Digital twins in safety analysis, risk assessment and emergency management," Reliability Engineering and System Safety, Elsevier, vol. 246(C).

    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:gam:jeners:v:15:y:2022:i:20:p:7697-:d:946195. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.