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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.
Gong et al. (Mon,) studied this question.