# Deep Neural Operator Driven Real Time Inference for Nuclear Systems to Enable Digital Twin Solutions arXiv: https://arxiv.org/abs/2308.07523 ยท HTML: https://mlsanity.com/paper/2308.07523/ ## Key facts - Cited by 22 papers in the map (data through 14 Oct 2026). - Builds on 9 of its 29 references that are in the map. - First posted on arXiv 15 Aug 2023. ## Builds on (most cited first, 9 of 9) - [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019) - [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019) - [A physics-informed variational DeepONet for predicting the crack path in brittle materials](https://mlsanity.com/paper/2108.06905/) (2021) - [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) - [Leveraging Industry 4.0 -- Deep Learning, Surrogate Model and Transfer Learning with Uncertainty Quantification Incorporated into Digital Twin for Nuclear System](https://mlsanity.com/paper/2210.00074/) (2022) - [Prediction and Uncertainty Quantification of SAFARI-1 Axial Neutron Flux Profiles with Neural Networks](https://mlsanity.com/paper/2211.08654/) (2022) - [Digital Twin-Centered Hybrid Data-Driven Multi-Stage Deep Learning Framework for Enhanced Nuclear Reactor Power Prediction](https://mlsanity.com/paper/2211.13157/) (2022) - [Digital Twin and Artificial Intelligence Incorporated With Surrogate Modeling for Hybrid and Sustainable Energy Systems](https://mlsanity.com/paper/2210.00073/) (2022) ## Built on by (most cited first, 22 of 22) - [Virtual Sensing-Enabled Digital Twin Framework for Real-Time Monitoring of Nuclear Systems Leveraging Deep Neural Operators](https://mlsanity.com/paper/2410.13762/) (2024) - [Geometry-Informed Neural Operator Transformer](https://mlsanity.com/paper/2504.19452/) (2025) - [Structure-Preserving Digital Twins via Conditional Neural Whitney Forms](https://mlsanity.com/paper/2508.06981/) (2025) - [From Proxies to Fields: Spatiotemporal Reconstruction of Global Radiation from Sparse Sensor Sequences](https://mlsanity.com/paper/2506.12045/) (2025) - [Physics-Informed Time-Integrated DeepONet: Temporal Tangent Space Operator Learning for High-Accuracy Inference](https://mlsanity.com/paper/2508.05190/) (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) - [Constrained Sensing and Reliable State Estimation with Shallow Recurrent Decoders on a TRIGA Mark II Reactor](https://mlsanity.com/paper/2510.12368/) (2025) - [Deep Neural ODE Operator Networks for PDEs](https://mlsanity.com/paper/2510.15651/) (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) - [Artificial Intelligence in Reactor Physics: Current Status and Future Prospects](https://mlsanity.com/paper/2503.02440/) (2025) - [SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving](https://mlsanity.com/paper/2604.11625/) (2026) - [Neuromorphic Continual Learning for Sequential Deployment of Nuclear Plant Monitoring Systems](https://mlsanity.com/paper/2604.18611/) (2026) - [Sensing Without Colocation: Operator-Based Virtual Instrumentation for Domains Beyond Physical Reach](https://mlsanity.com/paper/2510.18041/) (2025) - [Validation-Gated Multi-Agent Governance for Online Adaptation of Thermal-Hydraulic Surrogate Models under Operating-Regime Shift](https://mlsanity.com/paper/2606.03321/) (2026) - [Neural Operator Surrogates for Two-Dimensional Neutron Flux Estimation](https://mlsanity.com/paper/2607.19388/) (2026) - [Learning to Resolve Neutron Resonances with Fully Convolutional Neural Networks](https://mlsanity.com/paper/2608.04027/) (2026) - [Adapting neural operators for mechanics decisions under changing operating conditions](https://mlsanity.com/paper/2609.33978/) (2026) - [PTNO: Training Neural Operators with Noisy Monte Carlo Estimates for Particle Transport Problems](https://mlsanity.com/paper/2609.40090/) (2026) ## Abstract (arXiv) This paper focuses on the feasibility of Deep Neural Operator (DeepONet) as a robust surrogate modeling method within the context of digital twin (DT) for nuclear energy systems. Through benchmarking and evaluation, this study showcases the generalizability and computational efficiency of DeepONet in solving a challenging particle transport problem. DeepONet also exhibits remarkable prediction accuracy and speed, outperforming traditional ML methods, making it a suitable algorithm for real-time DT inference. However, the application of DeepONet also reveals challenges related to optimal sensor placement and model evaluation, critical aspects of real-world implementation. Addressing these challenges will further enhance the method's practicality and reliability. Overall, DeepONet presents a promising and transformative nuclear engineering research and applications tool. Its accurate prediction and computational efficiency capabilities can revolutionize DT systems, advancing nuclear engineering research. This study marks an important step towards harnessing the power of surrogate modeling techniques in critical engineering domains.