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The digital twin system of nuclear reactors is the foundation for the intelligent operation and maintenance of reactors and the visualization of operational data. Because of the current problem of low computational accuracy and lack of interpretability of deep learning algorithms for complex physical fields, this paper designs a deep learning and numerical analysis fusion algorithm based on a time series convolutional neural network algorithm, which can be used to solve the neutron diffusion spatiotemporal kinetics equation. The algorithm is based on convolutional neural network architecture, using finite volume method, constructing fixed parameter convolution kernel, and reconstructing loss function to replace convolutional neural network structure. This algorithm retains the convolutional neural network's structure and ensures that all steps have clear physical meaning. Finally, the algorithm logic and GPU acceleration are implemented on the Pytorch platform, and the algorithm's feasibility is verified using the simplified Tsinghua High Flux Reactor(THFR). The results show that the relative errors between the time series convolutional neural network and OpenMC in calculating the neutron flux density and the fission reaction rate are approximately within the range of 1% to 5%. The calculation speed of the time series convolutional neural network for neutron flux density is 1/20 of OpenMC, and the calculation speed of the expansion matrix is 1/8 of the NumPy library. Therefore, the time series convolutional neural network not only ensures the accuracy of calculation and improves the speed of operation, but also ensures the interpretability of the algorithm. In addition to being used to solve the neutron diffusion spatiotemporal kinetics equation, this algorithm is mainly used to develop the virtual physics engine of the digital twin system. Using this algorithm to implement the virtual reality method of the neutron field provides theoretical guidance and algorithm support for the development of the THFR digital twin system. [ABSTRACT FROM AUTHOR]

• Incore detectors results better than ex-core detectors, blending them leads to highest accuracy. • ROM is applicable when direct measurement information is unavailable. • Bayesian principles play a crucial role for core digital twins under uncertain conditions. In constructing a digital twin for a nuclear reactor core, it is important to consider the influence of randomness from various sources. Data assimilation (DA) can combine time distribution observations with dynamic models to approximate the real state of a physical system. Machine learning (ML) and DA share similarities under the Bayesian framework, and using probabilistic ML may provide a way to improve or replace current DA techniques. This paper proposes using a probabilistic ML as Bayesian neural network (BNN) to solve an inverse problem of core monitoring and demonstrates its feasibility through a pressurized water reactor core simulation analysis. Model order reduction technology is also analyzed, and the feasibility and benefit of using it to achieve core monitoring under steady-state conditions is preliminarily verified and discussed. Future work will focus on improving estimation and prediction models under transient operating conditions by unifying DA and ML under the Bayesian framework. [ABSTRACT FROM AUTHOR]

In a recently developed Nearly Autonomous Management and Control (NAMAC) system, neural networks (NNs) are used to develop digital twins for diagnosis (DT-Ds). However, NNs are not usually considered extrapolation models and may result in large errors if they are applied to unseen data outside the training data (uncovered). In this study, we propose a data coverage assessment (DCA) to determine if the NN-based DT-Ds are extrapolated based on their epistemic uncertainty. The uncertainty quantification algorithms and uncertainty thresholds are selected based on the confusion matrix of classifying evaluation data into covered or uncovered data. To demonstrate the adaptability of the proposed framework, we applied it to a basic feedforward neural network and a more advanced recurrent neural network based on a more nonlinear database. Case studies show that the proposed framework can distinguish unseen data for both basic and advanced applications with proper uncertainty quantification algorithms and thresholds. • Assess the data coverage of NN-based DTs to determine if they are extrapolated. • Test cases on FNNs and RNNs to demonstrate the adaptability of the framework. • The framework can distinguish unseen data with proper UQ algorithms and thresholds. [ABSTRACT FROM AUTHOR]

Reactor Operation Digital Twin (RODT) is now receiving increasing attention and investment in nuclear engineering domain. A prototype of a RODT was first brought out by Gong et al. at Nuclear Power Institute of China. The RODT contains a forward solver for online real-time simulation and an inverse problem solver for parameter identification and state estimation. To further improve the efficiency and accuracy of RODT and promote the practical deployment of RODT (i) we first propose an advanced differential evolution algorithm to upgrade the inverse solver; (ii) then we bring out a systematical uncertainty quantification of RODT considering assimilation noisy observations. The accuracy and validity of the proposed RODT are tested along one cycle operating stage of HPR1000, at various operating temperatures, control rod steps, general power level and the inlet temperature of a practical nuclear reactor core. Numerous numerical results confirm its potential for practical engineering applications for on-line parameter identification and state estimation. • An advanced differential evolution algorithm is implemented into the proposed RODT. • Observation denoising is realized with PCA followed by a normalization process. • Numerical tests on HPR1000 proof its efficiency and accuracy of the improved RODT. [ABSTRACT FROM AUTHOR]

• Development of prognosis digital twin with LSTM recurrent network. • Improvement of prognosis digital twin for better prediction and decision-making. • Investigation of manual search, Bayesian approach, and physics-guided ML. The nearly autonomous management and control (NAMAC) system is a comprehensive control system to assist plant operations by furnishing control recommendations to operators. Prognosis digital twin (DT-P) is a critical component in NAMAC for predicting action effects and supporting NAMAC decision-making during normal and accident scenarios. To quantifying and reducing uncertainty of machine-learning-based DT-Ps in multi-step predictions, this work investigates and derives insights from the application of three techniques for optimizing the performance of DT-P by long short-term memory recurrent neural networks, including manual search, sequential model-based optimization, and physics-guided machine learning. Sequential model-based optimization and physics-guide machine learning result in smallest errors when the predicting transients are similar to the training data. [ABSTRACT FROM AUTHOR]

This paper proposes an approach that combines reduced-order models with machine learning in order to create an digital twin to predict the power distribution over the core during the operation stage. The operational digital twin is designed to solve forward problems given input operation parameters, as well as to solve inverse problems given some observations of the power field. The forward model is non-intrusive and realised using SVD autoencoder reduced order model with the combination of machine learning methods, namely, k-nearest-neighbours and decision trees to build the input–output map. For model parameter estimation, the inverse model is based on a generalised latent assimilation method. The proposed approach is able to make use of the non intrusive reduced order model and the online measurements of the power field. The effectiveness in the sense of accuracy and real-time solver of the digital twin is illustrated through a real engineering problem in nuclear reactor physics — reactor core simulation in the life cycle of HPR1000 affected by input parameters, i.e., control rod inserting step, burnup, power level and inlet temperature of the coolant, which shows potential applications for on-line monitoring purpose. • A real-time operational digital twin is proposed for the prediction of power field in the core. • A non-intrusive forward model is built based on SVD-autoencoder and machine learning prediction methods. • An inverse model is realised based on a generalised latent assimilation method to overcome the bottleneck of efficient parameter identification. [ABSTRACT FROM AUTHOR]