Virtual Sensing-Enabled Digital Twin Framework for Real-Time Monitoring of Nuclear Systems Leveraging Deep Neural Operators

TL;DR

The paper addresses real-time monitoring in nuclear reactors where physical sensors are limited by harsh environments, proposing a DeepONet-based digital twin to serve as a dynamic, virtual sensing framework. It learns operator mappings $G_i$ from input functions $u$ (e.g., inlet velocity) to spatial fields $G_i(u)(y)$ for pressure, velocity, and turbulence in the AP-1000 hot leg, with per-parameter linear refiners to boost accuracy. Results show high predictive accuracy (low MSE and Relative $L_2$ error) and near real-time inference (≈0.135 s), achieving speedups of roughly $10^3$–$10^4$ over conventional CFD, enabling synchronization with the physical system. The framework supports degradation-aware monitoring and proactive maintenance, and demonstrates robustness to data splits and reduced mesh sizes, though limitations such as spectral bias in turbulence are noted, with future work pointing toward diffusion-based neural operators and hybrid region-specific models.

Abstract

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.

Figures (9)

• Figure 1: Schematic diagram of AP-1000 reactor coolant system Namgung_16.
• Figure 2: Computational domain and boundary conditions
• Figure 3: Grid generation over the domain
• Figure 4: Schematic of the FNN-based DeepONet architecture used in this study. The model consists of a single branch and trunk network. The branch network takes the average inlet velocity ($u$) as input, and the trunk network takes the spatial domain coordinates ($x, y, z$). The output quantities are distributions of coolant pressure ($P$), velocity ($V_o$), and turbulence kinetic energy ($k$). The schematic (a) shows the original DeepONet architecture. The Branch network has 11 hidden layers and the trunk network has 10 hidden layeres with 4096 neurons each. (b) The schemetic illustrates the modified architecture with additional linear layers for each parameter. The branch network has layer sizes of $[n, 512, 512, 512, N]$ where $n=1$, and the trunk network has layer sizes of $[3, 512, 512, 256, 3]$, both utilizing ReLU activation. At the end, there are three linear layers, each with sizes $[N, N]$, where $N=11,340$, without any activation.
• Figure 5: Histograms of original and scaled parameter values. The top row displays the original values for turbulence, pressure, and velocity, showing distinct distributions. The bottom row presents the values after min-max scaling, normalizing all parameters to the [0,1] range.