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

Konstantinos Prantikos, Lefteri H. Tsoukalas and Alexander Heifetz ()
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Konstantinos Prantikos: School of Nuclear Engineering, Purdue University, West Lafayette, IN 47906, 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

Energies, 2022, vol. 15, issue 20, 1-22

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.

Keywords: physics-informed neural networks; point kinetics equations; nuclear reactor; stiff ordinary differential equations; digital twin; nuclear reactor monitoring (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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