Syed Bahauddin Alam

James Daniell, Kazuma Kobayashi, Ayodeji Alajo et al.

The accurate and efficient modeling of nuclear reactor transients is crucial for ensuring safe and optimal reactor operation. Traditional physics-based models, while valuable, can be computationally intensive and may not fully capture the complexities of real-world reactor behavior. This paper introduces a novel hybrid digital twin-focused multi-stage deep learning framework that addresses these limitations, offering a faster and more robust solution for predicting the final steady-state power of reactor transients. By leveraging a combination of feed-forward neural networks with both classification and regression stages, and training on a unique dataset that integrates real-world measurements of reactor power and controls state from the Missouri University of Science and Technology Reactor (MSTR) with noise-enhanced simulated data, our approach achieves remarkable accuracy (96% classification, 2.3% MAPE). The incorporation of simulated data with noise significantly improves the model's generalization capabilities, mitigating the risk of overfitting. Designed as a digital twin supporting system, this framework integrates real-time, synchronized predictions of reactor state transitions, enabling dynamic operational monitoring and optimization. This innovative solution not only enables rapid and precise prediction of reactor behavior but also has the potential to revolutionize nuclear reactor operations, facilitating enhanced safety protocols, optimized performance, and streamlined decision-making processes. By aligning data-driven insights with the principles of digital twins, this work lays the groundwork for adaptable and scalable solutions in nuclear system management.

Kazuma Kobayashi, Syed Bahauddin Alam

Artificial intelligence (AI) and Machine learning (ML) are increasingly used in energy and engineering systems, but these models must be fair, unbiased, and explainable. It is critical to have confidence in AI's trustworthiness. ML techniques have been useful in predicting important parameters and in improving model performance. However, for these AI techniques to be useful for making decisions, they need to be audited, accounted for, and easy to understand. Therefore, the use of explainable AI (XAI) and interpretable machine learning (IML) is crucial for the accurate prediction of prognostics, such as remaining useful life (RUL), in a digital twin system, to make it intelligent while ensuring that the AI model is transparent in its decision-making processes and that the predictions it generates can be understood and trusted by users. By using AI that is explainable, interpretable, and trustworthy, intelligent digital twin systems can make more accurate predictions of RUL, leading to better maintenance and repair planning, and ultimately, improved system performance. The objective of this paper is to explain the ideas of XAI and IML and to justify the important role of AI/ML in the digital twin framework and components, which requires XAI to understand the prediction better. This paper explains the importance of XAI and IML in both local and global aspects to ensure the use of trustworthy AI/ML applications for RUL prediction. We used the RUL prediction for the XAI and IML studies and leveraged the integrated Python toolbox for interpretable machine learning~(PiML).

Kazuma Kobayashi, Syed Bahauddin Alam

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.

Kazuma Kobayashi, James Daniell, Syed Bahauddin Alam

Neural Operator Networks (ONets) represent a novel advancement in machine learning algorithms, offering a robust and generalizable alternative for approximating partial differential equations (PDEs) solutions. Unlike traditional Neural Networks (NN), which directly approximate functions, ONets specialize in approximating mathematical operators, enhancing their efficacy in addressing complex PDEs. In this work, we evaluate the capabilities of Deep Operator Networks (DeepONets), an ONets implementation using a branch/trunk architecture. Three test cases are studied: a system of ODEs, a general diffusion system, and the convection/diffusion Burgers equation. It is demonstrated that DeepONets can accurately learn the solution operators, achieving prediction accuracy scores above 0.96 for the ODE and diffusion problems over the observed domain while achieving zero shot (without retraining) capability. More importantly, when evaluated on unseen scenarios (zero shot feature), the trained models exhibit excellent generalization ability. This underscores ONets vital niche for surrogate modeling and digital twin development across physical systems. While convection-diffusion poses a greater challenge, the results confirm the promise of ONets and motivate further enhancements to the DeepONet algorithm. This work represents an important step towards unlocking the potential of digital twins through robust and generalizable surrogates.

M. Rahman, Abid Khan, Sayeed Anowar et al.

Industry 4.0 targets the conversion of the traditional industries into intelligent ones through technological revolution. This revolution is only possible through innovation, optimization, interconnection, and rapid decision-making capability. Numerical models are believed to be the key components of Industry 4.0, facilitating quick decision-making through simulations instead of costly experiments. However, numerical investigation of precise, high-fidelity models for optimization or decision-making is usually time-consuming and computationally expensive. In such instances, data-driven surrogate models are excellent substitutes for fast computational analysis and the probabilistic prediction of the output parameter for new input parameters. The emergence of Internet of Things (IoT) and Machine Learning (ML) has made the concept of surrogate modeling even more viable. However, these surrogate models contain intrinsic uncertainties, originate from modeling defects, or both. These uncertainties, if not quantified and minimized, can produce a skewed result. Therefore, proper implementation of uncertainty quantification techniques is crucial during optimization, cost reduction, or safety enhancement processes analysis. This chapter begins with a brief overview of the concept of surrogate modeling, transfer learning, IoT and digital twins. After that, a detailed overview of uncertainties, uncertainty quantification frameworks, and specifics of uncertainty quantification methodologies for a surrogate model linked to a digital twin is presented. Finally, the use of uncertainty quantification approaches in the nuclear industry has been addressed.

William Howes, Jason Yoo, Kazuma Kobayashi et al.

Accurate sensing of spatially distributed physical fields typically requires dense instrumentation, which is often infeasible in real-world systems due to cost, accessibility, and environmental constraints. Physics-based solvers address this through direct numerical integration of governing equations, but their computational latency and power requirements preclude real-time use in resource-constrained monitoring and control systems. Here we introduce VIRSO (Virtual Irregular Real-Time Sparse Operator), a graph-based neural operator for sparse-to-dense reconstruction on irregular geometries, and a variable-connectivity algorithm, Variable KNN (V-KNN), for mesh-informed graph construction. Unlike prior neural operators that treat hardware deployability as secondary, VIRSO reframes inference as measurement: the combination of both spectral and spatial analysis provides accurate reconstruction without the high latency and power consumption of previous graph-based methodologies with poor scalability, presenting VIRSO as a potential candidate for edge-constrained, real-time virtual sensing. We evaluate VIRSO on three nuclear thermal-hydraulic benchmarks of increasing geometric and multiphysics complexity, across reconstruction ratios from 47:1 to 156:1. VIRSO achieves mean relative $L_2$ errors below 1%, outperforming other benchmark operators while using fewer parameters. The full 10-layer configuration reduces the energy-delay product (EDP) from ${\approx}206$ J$\cdot$ms for the graph operator baseline to $10.1$ J$\cdot$ms on an NVIDIA H200. Implemented on an NVIDIA Jetson Orin Nano, all configurations of VIRSO provide sub-10 W power consumption and sub-second latency. These results establish the edge-feasibility and hardware-portability of VIRSO and present compute-aware operator learning as a new paradigm for real-time sensing in inaccessible and resource-constrained environments.

Md. Shamim Hassan, Abid Hossain Khan, Richa Verma et al.

The concept of small modular reactor has changed the outlook for tackling future energy crises. This new reactor technology is very promising considering its lower investment requirements, modularity, design simplicity, and enhanced safety features. The application of artificial intelligence-driven multi-scale modeling (neutronics, thermal hydraulics, fuel performance, etc.) incorporating Digital Twin and associated uncertainties in the research of small modular reactors is a recent concept. In this work, a comprehensive study is conducted on the multiscale modeling of accident-tolerant fuels. The application of these fuels in the light water-based small modular reactors is explored. This chapter also focuses on the application of machine learning and artificial intelligence in the design optimization, control, and monitoring of small modular reactors. Finally, a brief assessment of the research gap on the application of artificial intelligence to the development of high burnup composite accident-tolerant fuels is provided. Necessary actions to fulfill these gaps are also discussed.

Abid Hossain Khan, Salauddin Omar, Nadia Mushtary et al.

Surrogate modeling has brought about a revolution in computation in the branches of science and engineering. Backed by Artificial Intelligence, a surrogate model can present highly accurate results with a significant reduction in computation time than computer simulation of actual models. Surrogate modeling techniques have found their use in numerous branches of science and engineering, energy system modeling being one of them. Since the idea of hybrid and sustainable energy systems is spreading rapidly in the modern world for the paradigm of the smart energy shift, researchers are exploring the future application of artificial intelligence-based surrogate modeling in analyzing and optimizing hybrid energy systems. One of the promising technologies for assessing applicability for the energy system is the digital twin, which can leverage surrogate modeling. This work presents a comprehensive framework/review on Artificial Intelligence-driven surrogate modeling and its applications with a focus on the digital twin framework and energy systems. The role of machine learning and artificial intelligence in constructing an effective surrogate model is explained. After that, different surrogate models developed for different sustainable energy sources are presented. Finally, digital twin surrogate models and associated uncertainties are described.

Samrendra Roy, Kazuma Kobayashi, Souvik Chakraborty et al.

Continual learning, the ability to acquire new tasks sequentially without forgetting prior knowledge, is essential for deploying neural networks in dynamic real-world environments, from nuclear digital twin monitoring to grid-edge fault detection. Existing synaptic importance methods, such as Elastic Weight Consolidation (EWC) and Synaptic Intelligence (SI), rely on gradient computation, making them incompatible with neuromorphic hardware that lacks backpropagation support. We propose ISI-CV, the first gradient-free synaptic importance metric for SNN continual learning, derived from the Coefficient of Variation (CV) of Inter-Spike Intervals (ISIs). Neurons that fire regularly (low CV) encode stable, task-relevant features and are protected from overwriting; neurons with irregular firing are permitted to adapt freely. ISI-CV requires only spike time counters and integer arithmetic, all of which are native to every neuromorphic chip. We evaluate on four benchmarks of increasing difficulty: Split-MNIST, Permuted-MNIST, Split-FashionMNIST, and Split-N-MNIST using real Dynamic Vision Sensor (DVS) event data. Across three seeds, ISI-CV achieves zero forgetting (AF = 0.000 +/- 0.000) on Split-MNIST and Split-FashionMNIST, near-zero forgetting on Permuted-MNIST (AF = 0.001 +/- 0.000), and the highest accuracy with the lowest forgetting on real neuromorphic DVS data (AA = 0.820 +/- 0.012, AF = 0.221 +/- 0.014). On N-MNIST, gradient-based methods produce unreliable importance estimates and perform worse than no regularization; ISI-CV avoids this failure by design.

Samrendra Roy, Syed Bahauddin Alam

Quantum feature maps offer expressive embeddings for classical learning tasks, and augmenting sparse identification of nonlinear dynamics (SINDy) with such features is a natural but unexplored direction. We introduce \textbf{Q-SINDy}, a quantum-kernel-augmented SINDy framework, and identify a specific failure mode that arises: \emph{coefficient cannibalization}, in which quantum features absorb coefficient mass that rightfully belongs to the polynomial basis, corrupting equation recovery. We derive the exact cannibalization-bias formula $Δξ_P = (P^\top P)^{-1}P^\top Q\,\hatξ_Q$ and prove that orthogonalizing quantum features against the polynomial column space at fit time eliminates this bias exactly. The claim is verified numerically to machine precision ($<10^{-12}$) on multiple systems. Empirically, across six canonical dynamical systems (Duffing, Van der Pol, Lorenz, Lotka-Volterra, cubic oscillator, Rössler) and three quantum feature map architectures (ZZ-angle encoding, IQP, data re-uploading), orthogonalized Q-SINDy consistently matches vanilla SINDy's structural recovery while uncorrected augmentation degrades true-positive rates by up to 100\%. A refined dynamics-aware diagnostic, $R^2_Q$ for $\dot X$, predicts cannibalization severity with statistical significance (Pearson $r=0.70$, $p=0.023$). An RBF classical-kernel control across 20 hyperparameter configurations fails more severely than any quantum variant, ruling out feature count as the cause. Orthogonalization remains robust under depolarizing hardware noise up to 2\% per gate, and the framework extends without modification to Burgers' equation.

Samrendra Roy, Souvik Chakraborty, Rizwan-uddin et al.

Neural operators have emerged as powerful surrogates for partial differential equation (PDE) solvers, yet they are typically trained as monolithic models for individual PDEs, require energy-intensive GPU hardware, and must be retrained from scratch when new physics emerge. We introduce the Spiking Compositional Neural Operator (SCNO), a modular architecture combining spiking and conventional components that addresses all three limitations. SCNO maintains a library of small spiking neural operator blocks, each trained on a single elementary differential operator (convection, diffusion, reaction), and composes them through a lightweight input-conditioned aggregator to solve coupled PDEs not seen during block training. A small correction network learns cross-coupling residuals while keeping all blocks and the aggregator frozen, preserving zero-forgetting modular expansion by construction. We evaluate SCNO on eight PDE families including five coupled systems and a nuclear-relevant 1-group neutron diffusion equation. SCNO with correction achieves the lowest relative $L^2$ error on four of five coupled PDEs, outperforming both a monolithic spiking DeepONet (by up to 62%, mean over 3 seeds) and a standard ANN DeepONet (by up to 65%), while requiring only 95K trainable parameters versus 462K for the monolithic baseline. To our knowledge, this is the first compositional spiking neural operator and the first proof-of-concept for modular neuromorphic PDE solving with built-in forgetting-free expansion.

Samrendra Roy, Sajedul Talukder, Syed Bahauddin Alam

Anomaly detection in nuclear industrial control systems (ICS) requires continuous, energy-efficient monitoring across multiple subsystems that are often deployed at different stages of plant commissioning. When a conventional neural network is sequentially trained to monitor new subsystems, it catastrophically forgets previously learned anomaly patterns, a safety-critical failure mode. We present the first spiking neural network (SNN)-based anomaly detection system with continual learning for nuclear ICS, addressing both challenges simultaneously. Our approach introduces spike-encoded asynchronous sensor fusion, a delta-based encoding that converts heterogeneous sensor streams into sparse spike trains at rates dictated by each sensor's natural dynamics, achieving 92.7% input sparsity. We evaluate five continual learning strategies, including sequential fine-tuning, Elastic Weight Consolidation (EWC), Synaptic Intelligence (SI), experience replay, and a hybrid EWC+Replay approach, on the HAI 21.03 nuclear ICS security dataset across three sequentially deployed subsystems (boiler, turbine, water treatment). The hybrid EWC+Replay method achieves an average F1 score of 0.979 with near-zero average forgetting (AF = 0.000 single seed; 0.035 +/- 0.039 across three seeds), while requiring 12.6x fewer operations (an estimated 2.5x in energy based on published hardware specifications) than an equivalent artificial neural network. The system detects all tested attacks with a mean latency of 0.6 seconds. These results demonstrate that neuromorphic computing offers a viable path toward always-on, energy-efficient, and adaptable safety monitoring for next-generation nuclear facilities.

Jiwoon Lee, Souvik Chakraborty, Syed Bahauddin Alam et al.

Low-cost FPGA platforms can broaden access to neuromorphic systems research, but current spiking neural network (SNN) workflows remain divided between hardware-first implementations, which are difficult to integrate with PyTorch-style development, and software-first frameworks, which often stop at simulation or GPU execution. This paper presents a semantics-preserving hardware-software co-design framework for the deterministic deployment of PyTorch-defined SNNs to event-driven FPGA execution. A single exported artifact carries weights, thresholds, connectivity descriptors, and grouped time-to-first-spike (TTFS) decoding metadata from software definition to board execution and is reused unchanged by both the software reference and the board runtime. A 10-class MNIST TTFS classifier implemented in the routed 80 MHz design achieves 87.40\% accuracy and matches the software reference on all 10,000 test images. The programmable-logic path delivers a service latency of 0.1375 μs/image and an estimated dynamic energy of 31.6 nJ/image, while scope-aware comparisons with matched GPU and CPU baselines keep accelerator-only and system-level measurements distinct. These results show that low-cost event-driven FPGA hardware can provide a direct and reproducible software-to-board path for software-defined SNN models.

Jason Yoo, Shailesh Garg, Souvik Chakraborty et al.

Spiking neural operators are appealing for neuromorphic edge computing because event-driven substrates can, in principle, translate sparse activity into lower latency and energy. Whether that advantage survives deployment on commodity edge-GPU software stacks, however, remains unclear. We study this question on a Jetson Orin Nano 8 GB using five pretrained variable-spiking wavelet neural operator (VS-WNO) checkpoints and five matched dense wavelet neural operator (WNO) checkpoints on the Darcy rectangular benchmark. On a reference-aligned path, VS-WNO exhibits substantial algorithmic sparsity, with mean spike rates decreasing from 54.26% at the first spiking layer to 18.15% at the fourth. On a deployment-style request path, however, this sparsity does not reduce deployed cost: VS-WNO reaches 59.6 ms latency and 228.0 mJ dynamic energy per inference, whereas dense WNO reaches 53.2 ms and 180.7 mJ, while also achieving slightly lower reference-path error (1.77% versus 1.81%). Nsight Systems indicates that the request path remains launch-dominated and dense rather than sparsity-aware: for VS-WNO, cudaLaunchKernel accounts for 81.6% of CUDA API time within the latency window, and dense convolution kernels account for 53.8% of GPU kernel time; dense WNO shows the same pattern. On this Jetson-class GPU stack, spike sparsity is measurable but does not reduce deployed cost because the runtime does not suppress dense work as spike activity decreases.

William Howes, Farid Ahmed, Kazuma Kobayashi et al.

Predicting full-field physics through the real-time virtual sensing of engineering systems can enhance limited physical sensors but often requires sparse-to-dense reconstruction, complex multiphysics, and highly irregular geometries as well as strict latency and energy constraints for edge-deployability. Neural operators have been presented as a potential candidate for such applications but few architectures exist that explicitly address power consumption. Spiking neuron integration can provide a potential solution when integrated on neuromorphic hardware but the current existing neuron models result in severe performance degradation towards regression-based virtual sensing. To address the performance concerns and edge-constraints, we present the Variable Spiking Graph Neural Operator (VS-GNO) which integrates a sophisticated spectral-spatial convolutional analysis and a previously developed Variable Spiking Neuron (VSN) and energy-error balance loss function. With a non-spiking $L_2$ error baseline of $0.4\%$, VS-GNO can provide a reconstruction error of $0.71\%$ with $15\%$ average spiking in its spectral-only form and $1.04\%$ with $24.5\%$ spiking in its entire form. These results position VS-GNO as a promising step towards energy-efficient, edge-deployable neural operators for real-time sparse-to-dense virtual sensing in complex, highly irregular engineering environments.

Raisa Bentay Hossain, Farid Ahmed, Kazuma Kobayashi et al.

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.

Jay Phil Yoo, William Howes, Yashika Ghai et al.

Real-time reconstruction of magnetohydrodynamic equilibria is essential for plasma shaping, stability assessment and feedback control in magnetic confinement fusion. However, Grad-Shafranov equilibrium calculations remain largely device-specific and iterative, limiting their use in latency-constrained control settings. Existing neural approaches can accelerate individual equilibrium predictions, but they do not generally provide reusable models across changing plasma boundaries or tokamak geometries. Here we show that equilibrium reconstruction can be recast as a cross-device operator learning problem. We develop a domain-specific neural operator framework that maps geometry and profile parameters directly to the poloidal flux field, replacing repeated solve-on-demand computation with amortized operator inference. Using the analytically tractable Solov'ev family as a controlled Grad-Shafranov testbed, we generate equilibria across eight geometrically distinct tokamak-like configurations and benchmark five neural operator architectures under four transfer-learning strategies. Single-geometry pretraining gives poor transfer to unseen devices, whereas multi-geometry pretraining enables data-efficient adaptation. The Wavelet Neural Operator gives the strongest cross-geometry performance, reaching mean relative L2 errors below 4% with 100 labelled target equilibria and below 2% with full fine-tuning. The predicted magnetic fields satisfy the divergence-free constraint to numerical precision, and four architectures achieve millisecond or sub-millisecond inference. These results identify neural operator pretraining as a route towards reusable, real-time equilibrium inference across fusion device configurations.

Kazuma Kobayashi, Samrendra Roy, Seid Koric et al.

Accurate reconstruction of latent environmental fields from sparse and indirect observations is a foundational challenge across scientific domains-from atmospheric science and geophysics to public health and aerospace safety. Traditional approaches rely on physics-based simulators or dense sensor networks, both constrained by high computational cost, latency, or limited spatial coverage. We present the Temporal Radiation Operator Network (TRON), a spatiotemporal neural operator architecture designed to infer continuous global scalar fields from sequences of sparse, non-uniform proxy measurements. Unlike recent forecasting models that operate on dense, gridded inputs to predict future states, TRON addresses a more ill-posed inverse problem: reconstructing the current global field from sparse, temporally evolving sensor sequences, without access to future observations or dense labels. Demonstrated on global cosmic radiation dose reconstruction, TRON is trained on 22 years of simulation data and generalizes across 65,341 spatial locations, 8,400 days, and sequence lengths from 7 to 90 days. It achieves sub-second inference with relative L2 errors below 0.1%, representing a >58,000X speedup over Monte Carlo-based estimators. Though evaluated in the context of cosmic radiation, TRON offers a domain-agnostic framework for scientific field reconstruction from sparse data, with applications in atmospheric modeling, geophysical hazard monitoring, and real-time environmental risk forecasting.

Kazuma Kobayashi, Farid Ahmed, Syed Bahauddin Alam

Real-time monitoring of critical parameters is essential for energy systems' safe and efficient operation. However, traditional sensors often fail and degrade in harsh environments where physical sensors cannot be placed (inaccessible locations). In addition, there are important parameters that cannot be directly measured by sensors. We need machine learning (ML)-based real-time monitoring in those remote locations to ensure system operations. However, traditional ML models struggle to process continuous sensor profile data to fit model requirements, leading to the loss of spatial relationships. Another challenge for real-time monitoring is ``dataset shift" and the need for frequent retraining under varying conditions, where extensive retraining prohibits real-time inference. To resolve these challenges, this study addressed the limitations of real-time monitoring methods by enabling monitoring in locations where physical sensors are impractical to deploy. Our proposed approach, utilizing Multi-Input Operator Network virtual sensors, leverages deep learning to seamlessly integrate diverse data sources and accurately predict key parameters in real-time without the need for additional physical sensors. The approach's effectiveness is demonstrated through thermal-hydraulic monitoring in a nuclear reactor subchannel, achieving remarkable accuracy.

Jay Phil Yoo, Kazuma Kobayashi, Souvik Chakraborty et al.

Forecasting unobservable physical quantities from sparse, cross-domain sensor data is a central unsolved problem in scientific machine learning. Existing neural operators and large-scale forecasters rely on dense, co-located input-output fields and short temporal contexts, assumptions that fail in real-world systems where sensing and prediction occur on distinct physical manifolds and over long timescales. We introduce the Spatio-Temporal Operator Network (STONe), a non-autoregressive neural operator that learns a stable functional mapping between heterogeneous domains. By directly inferring high-altitude radiation dose fields from sparse ground-based neutron measurements, STONe demonstrates that operator learning can generalize beyond shared-domain settings. It defines a nonlinear operator between sensor and target manifolds that remains stable over long forecasting horizons without iterative recurrence. This challenges the conventional view that operator learning requires domain alignment or autoregressive propagation. Trained on 23 years of global neutron data, STONe achieves accurate 180-day forecasts with millisecond inference latency. The framework establishes a general principle for cross-domain operator inference, enabling real-time prediction of complex spatiotemporal fields in physics, climate, and energy systems.

Kazuma Kobayashi, Shailesh Garg, Farid Ahmed et al.

Robust uncertainty quantification (UQ) remains a critical barrier to the safe deployment of deep learning in real-time virtual sensing, particularly in high-stakes domains where sparse, noisy, or non-collocated sensor data are the norm. We introduce the Conformalized Monte Carlo Operator (CMCO), a framework that transforms neural operator-based virtual sensing with calibrated, distribution-free prediction intervals. By unifying Monte Carlo dropout with split conformal prediction in a single DeepONet architecture, CMCO achieves spatially resolved uncertainty estimates without retraining, ensembling, or custom loss design. Our method addresses a longstanding challenge: how to endow operator learning with efficient and reliable UQ across heterogeneous domains. Through rigorous evaluation on three distinct applications: turbulent flow, elastoplastic deformation, and global cosmic radiation dose estimation-CMCO consistently attains near-nominal empirical coverage, even in settings with strong spatial gradients and proxy-based sensing. This breakthrough offers a general-purpose, plug-and-play UQ solution for neural operators, unlocking real-time, trustworthy inference in digital twins, sensor fusion, and safety-critical monitoring. By bridging theory and deployment with minimal computational overhead, CMCO establishes a new foundation for scalable, generalizable, and uncertainty-aware scientific machine learning.

Kazuma Kobayashi, Jaewan Park, Qibang Liu et al.

Scientific applications increasingly demand real-time surrogate models that can capture the behavior of strongly coupled multiphysics systems driven by multiple input functions, such as in thermo-mechanical and electro-thermal processes. While neural operator frameworks, such as Deep Operator Networks (DeepONets), have shown considerable success in single-physics settings, their extension to multiphysics problems remains poorly understood. In particular, the challenge of learning nonlinear interactions between tightly coupled physical fields has received little systematic attention. This study addresses a foundational question: should the architectural design of a neural operator reflect the strength of physical coupling it aims to model? To answer this, we present the first comprehensive, architecture-aware evaluation of DeepONet variants across three regimes: single-physics, weakly coupled, and strongly coupled multiphysics systems. We consider a reaction-diffusion equation with dual spatial inputs, a nonlinear thermo-electrical problem with bidirectional coupling through temperature-dependent conductivity, and a viscoplastic thermo-mechanical model of steel solidification governed by transient phase-driven interactions. Two operator-learning frameworks, the classical DeepONet and its sequential GRU-based extension, S-DeepONet, are benchmarked using both single-branch and multi-branch (MIONet-style) architectures. Our results demonstrate that architectural alignment with physical coupling is crucial: single-branch networks significantly outperform multi-branch counterparts in strongly coupled settings, whereas multi-branch encodings offer advantages for decoupled or single-physics problems. Once trained, these surrogates achieve full-field predictions up to 1.8e4 times faster than high-fidelity finite-element solvers, without compromising solution accuracy.