Effective real-time monitoring is a foundation of digital twin technology, crucial for detecting material degradation and maintaining the structural integrity of nuclear systems to ensure both safety and operational efficiency. Traditional physical sensor systems face limitations such as installation challenges, high costs, and difficulty measuring critical parameters in hard-to-reach or harsh environments, often resulting in incomplete data coverage. Machine learning-driven virtual sensors, integrated within a digital twin framework, offer a transformative solution by enhancing physical sensor capabilities to monitor critical degradation indicators like pressure, velocity, and turbulence. However, conventional machine learning models struggle with real-time monitoring due to the high-dimensional nature of reactor data and the need for frequent retraining. This paper introduces the use of Deep Operator Networks (DeepONet) as a core component of a digital twin framework to predict key thermal-hydraulic parameters in the hot leg of an AP-1000 Pressurized Water Reactor (PWR). DeepONet serves as a dynamic and scalable virtual sensor by accurately mapping the interplay between operational input parameters and spatially distributed system behaviors. In this study, DeepONet is trained with different operational conditions, which relaxes the requirement of continuous retraining, making it suitable for online and real-time prediction components for digital twin. Our results show that DeepONet achieves accurate predictions with low mean squared error and relative L2 error and can make predictions on unknown data 1400 times faster than traditional CFD simulations. This speed and accuracy enable DeepONet to synchronize with the physical system in real-time, functioning as a dynamic virtual sensor that tracks degradation-contributing conditions.

翻译：有效的实时监测是数字孪生技术的基础，对于检测材料退化、维持核系统结构完整性以确保安全与运行效率至关重要。传统的物理传感器系统面临安装困难、成本高昂以及在难以触及或恶劣环境中测量关键参数困难等局限，常导致数据覆盖不完整。集成于数字孪生框架内的机器学习驱动虚拟传感器，通过增强物理传感器监测压力、流速和湍流等关键退化指标的能力，提供了一种变革性解决方案。然而，传统机器学习模型因反应堆数据的高维特性及频繁再训练需求，难以胜任实时监测任务。本文提出将深度算子网络（DeepONet）作为数字孪生框架的核心组件，用于预测AP-1000压水堆热段的关键热工水力参数。DeepONet通过精确映射运行输入参数与空间分布系统行为间的相互作用，充当动态可扩展的虚拟传感器。在本研究中，DeepONet在不同运行条件下进行训练，这降低了对持续再训练的要求，使其适用于数字孪生的在线实时预测组件。我们的结果表明，DeepONet能以较低的均方误差和相对L2误差实现精确预测，且对未知数据的预测速度比传统CFD模拟快1400倍。这种速度与精度使DeepONet能够与物理系统实时同步，作为跟踪导致退化条件的动态虚拟传感器运行。