# Virtual Sensing-Enabled Digital Twin Framework for Real-Time Monitoring of Nuclear Systems Leveraging Deep Neural Operators arXiv: https://arxiv.org/abs/2410.13762 ยท HTML: https://mlsanity.com/paper/2410.13762/ ## Key facts - Cited by 12 papers in the map (data through 14 Oct 2026). - Builds on 14 of its 55 references that are in the map. - First posted on arXiv 17 Oct 2024. ## Builds on (most cited first, 14 of 14) - [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020) - [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019) - [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022) - [Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loads](https://mlsanity.com/paper/2306.08218/) (2023) - [Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling](https://mlsanity.com/paper/2409.08477/) (2024) - [Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads](https://mlsanity.com/paper/2306.03645/) (2023) - [Deep Neural Operator Driven Real Time Inference for Nuclear Systems to Enable Digital Twin Solutions](https://mlsanity.com/paper/2308.07523/) (2023) - [Explainable, Interpretable & Trustworthy AI for Intelligent Digital Twin: Case Study on Remaining Useful Life](https://mlsanity.com/paper/2301.06676/) (2023) - [Improved generalization with deep neural operators for engineering systems: Path towards digital twin](https://mlsanity.com/paper/2301.06701/) (2023) - [Graph Neural Networks for Virtual Sensing in Complex Systems: Addressing Heterogeneous Temporal Dynamics](https://mlsanity.com/paper/2407.18691/) (2024) - [Digital Twin-Centered Hybrid Data-Driven Multi-Stage Deep Learning Framework for Enhanced Nuclear Reactor Power Prediction](https://mlsanity.com/paper/2211.13157/) (2022) - [Physics-Enhanced Graph Neural Networks For Soft Sensing in Industrial Internet of Things](https://mlsanity.com/paper/2404.08061/) (2024) - [Virtual Sensor for Real-Time Bearing Load Prediction Using Heterogeneous Temporal Graph Neural Networks](https://mlsanity.com/paper/2404.02304/) (2024) - [A machine-learning approach to synthesize virtual sensors for parameter-varying systems](https://mlsanity.com/paper/2103.12324/) (2021) ## Built on by (most cited first, 12 of 12) - [From Models To Experiments: Shallow Recurrent Decoder Networks on the DYNASTY Experimental Facility](https://mlsanity.com/paper/2503.08907/) (2025) - [CTF4Nuclear: Common Task Framework for Nuclear Fission and Fusion Models](https://mlsanity.com/paper/2605.15549/) (2026) - [Real-Time Sensing of Inaccessible Physical Fields via an Edge-Deployable Hardware-Portable Graph Neural Operator](https://mlsanity.com/paper/2604.01802/) (2026) - [Distribution-Free Uncertainty-Aware Virtual Sensing via Conformalized Neural Operators](https://mlsanity.com/paper/2507.11574/) (2025) - [Agentic Physical AI toward a Domain-Specific Foundation Model for Energy Systems: A Case Study on Nuclear Reactor Control](https://mlsanity.com/paper/2512.23292/) (2025) - [Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systems](https://mlsanity.com/paper/2507.03660/) (2025) - [Beyond Uniform Sampling: Synergistic Active Learning and Input Denoising for Robust Neural Operators](https://mlsanity.com/paper/2604.13316/) (2026) - [Energy-efficient operation of neural operators for virtual sensing](https://mlsanity.com/paper/2609.30580/) (2026) - [Sensing Without Colocation: Operator-Based Virtual Instrumentation for Domains Beyond Physical Reach](https://mlsanity.com/paper/2510.18041/) (2025) - [Gradient-Free Continual Learning in Spiking Neural Networks via Inter-Spike Interval Regularization](https://mlsanity.com/paper/2604.16496/) (2026) - [Information Density as a Quantitative Measure for AI-enabled Virtual Sensing: Feasibility and Limits](https://mlsanity.com/paper/2605.08180/) (2026) - [NuclearDiffusion: Text-to-Image Foundation Models for Learning Nuclear Energy Concepts](https://mlsanity.com/paper/2608.04030/) (2026) ## Abstract (arXiv) 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.