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

Author

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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