Data-Enabled Physics-Informed Machine Learning for Reduced-Order Modeling Digital Twin: Application to Nuclear Reactor Physics

Abstract

This paper proposes an approach that combines reduced-order models with machine learning in order to create physics-informed digital twins to predict high-dimensional output quantities of interest, such as neutron flux and power distributions in nuclear reactor cores. The digital twin is designed to solve forward problems given input parameters, as well as to solve inverse problems given some extra measurements. Offline, we use reduced-order modeling, namely, the proper orthogonal decomposition, to assemble physics-based computational models that are accurate enough for the fast predictive digital twin. The machine learning techniques, namely, k-nearest-neighbors and decision trees, are used to formulate the input-parameter-dependent coefficients of the reduced basis, after which the high-fidelity fields are able to be reconstructed. Online, we use the real-time input parameters to rapidly reconstruct the neutron field in the core based on the adapted physics-based digital twin. The effectiveness of the framework is illustrated through a real engineering problem in nuclear reactor physics—reactor core simulation in the life cycle of the HPR1000 governed by the two-group neutron diffusion equations affected by input parameters, i.e., burnup, control rod inserting step, power level, and temperature of the coolant—which shows potential applications for online monitoring purposes.

Keywords:

• Digital twin
• model order reduction
• machine learning
• proper orthogonal decomposition
• nuclear reactor physics

Disclosure Statement

No potential conflict of interest was reported by the authors.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (11905216) and the Leverhulme Centre for Wildfires, Environment and Society through the Leverhulme Trust (RC-2018-023).

This work benefited from the helpful supervision of Yvon Maday, professor at Laboratoire Jacques-Louis Lions, Sorbonne Universités, UPMC Univ Paris 06, 4, Place Jussieu, 75005 Paris, France. This work also benefited from helpful discussions with Chuanju Xu, School of the Mathematical Modeling and High Performance Scientific Computing, Xiamen University, 361005 Xiamen, China. The authors are grateful to two anonymous reviewers for the useful remarks on the manuscript.

Code for the implementation of the KNN and DT forward prediction with hyper parameter tuning and inverse modelling is available at https://github.com/scheng1992/ML-for-predicting-POD-coefficients.