Abstract
Digital Twins (DTs) are emerging as powerful tools to enhance monitoring, maintenance, and safety assurance in nuclear power systems. This review synthesizes recent advances in the integration of DTs with artificial intelligence (AI) and machine learning (ML), emphasizing their application to condition monitoring, inservice testing, and inservice inspection. Case studies illustrate how DT frameworks, ranging from anomaly detection and fault classification to virtual sensing, can improve detection of early degradation, quantify severity, and extend observability into regions inaccessible to physical instrumentation. Collectively, these approaches demonstrate the potential of DTs to shift nuclear safety practices from periodic, schedule-based testing and inspection toward predictive and risk-informed strategies. The review also examines regulatory considerations, highlighting the challenges of qualifying AI/ML-enabled DTs.
1 Introduction and motivation
Advanced nuclear reactors promise enhanced safety, flexibility, and resilience, although their deployment needs to ensure alignment with regulatory pathways and the integration of advanced digital technologies to realize full potential. Digital Twins (DTs) has emerged as a transformative tool to support real-time system monitoring, predictive maintenance, and risk-informed decision-making. DTs offer a synchronized virtual representation of physical systems, integrating high-fidelity modeling with operational data to inform engineering and safety assessments.
This review examines recent advancements in the use of DTs to support the safe operation and effective integration of advanced technologies in both light-water reactors (LWRs) and non-light-water reactor (non-LWR) designs. Drawing on current research and case studies, it synthesizes examples to show how DT frameworks (including physics-based modeling and machine learning–driven virtual sensing) can complement and enhance established practices in inservice testing (IST), inservice inspection (ISI), and condition monitoring (CM). In doing so, the review highlights the potential for DTs to extend beyond schedule-based testing, enabling more predictive and risk-informed approaches to safety assurance.
2 Foundations of digital twins
A DT is a virtual representation of an entity that is continuously updated with data from the real system. The origin of DTs is rooted in the aerospace and manufacturing industries to model complex systems in real-time (). As a virtual representation, a DT leverages various types of models, data, and frameworks to produce knowledge and insights about the represented entity to fulfill an intended purpose (; ). The DT can be categorized by level of representation or functional purpose. The level of representation can be as granular as a single part (e.g., a pump seal), a whole component (e.g., a pump), a system where multiple components interact with one another, or it can be as broad as a process workflow that captures operations and industrial processes (). The functional purpose of a DT can be either descriptive, diagnostic, predictive, or prescriptive, with each stage adding greater analytical complexity and capability (). A descriptive twin uses its input data to mirror the state of its real-world counterpart. A diagnostic twin explains why something happens when an issue arises. A predictive twin uses predictive models to forecast future states or failures based on the input state data. Lastly, a prescriptive twin extends the predictive concept by suggesting optimal actions based on the current or projected system state (). In either of the diagnostic, predictive, or prescriptive functional roles, artificial intelligence and machine learning (AI/ML) models can be incorporated to strengthen diagnostics, predictions, or prescriptions. This progression from descriptive to prescriptive illustrates how DTs evolve in capability, culminating in systems that close the loop between sensing, analysis, prediction, and action.
The most comprehensive form of a DT is a prescriptive twin. For a nuclear power plant (NPP), a prescriptive DT system would broadly comprise of four elements: (1) a NPP with sensors throughout its physical assets to acquire data, (2) a DT model as the virtual representation, (3) data for a physical asset flowing from the NPP to the digital twin, and (4) actions and recommendations flowing from the DT to the NPP. As information flows from the NPP to the digital twin, that information is processed and analyzed through various methods (e.g., data analytics and data-informed models), and then ultimately returned to the NPP in useful forms such as diagnostics, visualizations, operation and maintenance (O&M) recommendations, and control signals. A visualization of this DT system for a nuclear power plant is captured in Figure 1 (; ).
FIGURE 1
While prescriptive DTs represent the most comprehensive form of the technology, their deployment in nuclear power remains conceptual. The primary barrier is not technical feasibility alone, but also regulatory acceptance, since existing frameworks do not yet specify how DTs should be validated, qualified, or incorporated into safety-related programs. Accordingly, progress in DT adoption will depend as much on regulatory frameworks as on technical capability.
3 Regulatory context for digital twins in U.S. nuclear power
In the United States, commercial nuclear power plants are required to comply with regulations set forth by the Nuclear Regulatory Commission (NRC) under Title 10 of the Code of Federal Regulations (10 CFR) (
Key opportunities for leveraging DTs in nuclear power lie in inservice testing and inservice inspection, which are mandated under 10 CFR 50.55a (
Condition monitoring (CM) within IST and ISI programs involves tracking equipment performance data—such as vibration, temperature, and pressure—to detect degradation that may challenge operability and safety requirements (
Research activities have increasingly examined how ACM can support compliance with IST and ISI requirements in nuclear power plants. Recent investigations have explored the feasibility of integrating AI/ML with DT technologies to assess component conditions, and case studies have demonstrated applications such as flaw detection in nuclear systems. Because AI/ML can be applied broadly across reactor performance tasks, it is essential to clearly understand both their capabilities and limitations before widespread adoption. Such understanding will also enable regulators to establish appropriate oversight and guidance, ensuring that DT applications enhance safety while maintaining credibility within regulatory frameworks. This review synthesizes these efforts, underscoring both the promise and the limitations of AI/ML-enabled DT approaches and their potential to contribute to regulatory credibility.
4 Insights from case studies on digital twins for nuclear condition monitoring
Recent work has investigated the use of advanced technologies to supplement IST and ISI for SSCs in both LWR and non-LWR contexts. These studies cover DTs with diagnostic, predictive, and prescriptive capabilities, with many leveraging simulated data to demonstrate feasibility while also underscoring practical implications for deployment. The subsections below review case studies for different applications of DTs, drawing connections between the different works and to a broader regulatory perspective.
4.1 BWR recirculation pump
The NRC has investigated the use of AI/ML to detect and classify anomalies in a boiling water reactor (BWR). A use case was developed to demonstrate and evaluate a data-driven, ML-based anomaly detector and classifier for a BWR recirculation pump. To investigate the feasibility of detection and classification, a BWR simulator was used to generate synthetic data for known conditions. Using synthetic data provided well-defined baselines against which to evaluate the AI/ML models. The objective was to determine whether these models could reliably detect and classify malfunctions from simulated multivariate time-series data representative of nuclear power plant operating conditions.
The scope of this work was limited to operational scenarios involving nominal steady-state full-power operating conditions in a BWR, with six simulated malfunction conditions affecting recirculation pump performance. Plant operating parameters were established based on expert judgement. The modeled malfunctions included pump runaway as well as upper and lower seal failures in each of two BWR recirculation pumps, providing six distinct cases. Monitoring parameters included reactor power, mass flow rate, and upper and lower seal pressure. Two types of models were developed and evaluated: an anomaly detection model and an anomaly classification model. The anomaly detection model was implemented as a long short-term memory (LSTM) autoencoder trained to learn nominal operating patterns, while the classification model was a stacked LSTM with a Softmax output layer trained under supervised learning to assign one of six recirculation pump malfunction types.
4.1.1 Simulation conditions
Two separate datasets were used, one for the detector and one for the classifier. For the anomaly detector, approximately 4 hours of full-power steady state data (1-s resolution) were used to train on normal operating conditions. To ensure the LSTM learned temporal patterns, sequence-to-sequence modeling (also known as time-series segmentation) was used, segmenting the data into overlapping sliding time windows. The window length was treated as a hyperparameter, with windows of 10, 15, and 20 s considered. Seven monitoring parameters were selected to define the baseline behavior, and the resulting windowed dataset was used to train the unsupervised LSTM-autoencoder to learn this behavior and detect deviations from it.
For the classifier, the dataset included multiple 60-s transients, each beginning from nominal full-power conditions with a malfunction introduced at 5 s. Each transient was labeled with its associated malfunction via one-hot encoding and used to train the classifier model. Malfunctions were simulated across a range of severities, generating hundreds of samples per malfunction. To create distinct training datasets, the 60-s transients were used in three forms: the full 60 s, truncated to 30 s, and truncated to 10 s. The resulting datasets were shuffled and split into training, validation, and testing subsets (80/10/10, respectively). Because the classifier was trained exclusively on malfunction data and not on nominal operation, it must be paired with the anomaly detector so that the detector first flags an anomaly, after which classification is applied.
4.1.2 Frameworks for predictive models
To evaluate the feasibility of AI/ML methods for monitoring BWR recirculation pumps, two complementary predictive models were developed: an anomaly detection model trained to identify deviations from normal operating conditions, and an anomaly classification model trained to distinguish among specific malfunction types once an anomaly was detected. Together, these frameworks form a pipeline where the detector first signals abnormal behavior, and the classifier then assigns the fault to a defined category.
4.1.2.1 Anomaly detection model
The anomaly detector was implemented as an LSTM-autoencoder trained to model short-term temporal patterns of nominal operation. The approach used input sequence reconstructions with mean squared error (MSE) as the anomaly signal. A conceptual autoencoder architecture used in this study is shown in Figure 2, highlighting the encoder-decoder nature of the framework.
FIGURE 2

Conceptual autoencoder architecture used for anomaly detector (
The architecture was comprised of four LSTM layers: the input sequence (seven features per time step across a 10-s, 15-s, or 20-s window) was processed through an encoder with 128 hidden units, compressed into a 64-unit latent space, and then decoded symmetrically back to 128 units before reconstructing the original input sequence. Window lengths of 10, 15, and 20 s were evaluated as hyperparameters to assess sensitivity to sequence duration.
The training stage used ∼14,878 samples (∼4 h of nominal steady-state data at 1-s resolution). The model was optimized to minimize reconstruction error, with MSE used as the loss function (
Once trained, the autoencoder achieved low reconstruction error on nominal conditions. When applied to transient datasets, deviations from the baseline reconstruction error consistently indicated the onset of anomalies.
4.1.2.2 Anomaly classification model
The anomaly classifier was implemented as an LSTM-Softmax model trained on the labeled transient datasets. The architecture is shown in Figure 3 and consists of stacked LSTM layers followed by a Softmax output layer for multiclass classification across the six malfunction types. The model was trained to minimize categorical cross-entropy loss using supervised learning (
FIGURE 3

Conceptual neural network architecture used for anomaly classifier (
Since the classifier was trained exclusively on malfunction data, it is unable to recognize nominal operation and always assigned a fault label. Its role is therefore complementary to the anomaly detector: the detector first signals that an anomaly is present, and the classifier then identifies the specific fault type.
4.1.3 Assessment of model performance
The effectiveness of the predictive models was assessed through quantitative performance evaluation. Results are presented for both the anomaly detection and classification frameworks, as well as for their combined application. The evaluation highlights detection sensitivity, classification accuracy, and overall robustness, while also noting practical limitations that affect deployment in operational settings.
The LSTM-autoencoder trained on nominal steady-state data successfully reconstructed normal sequences with low error and flagged deviations when faults were introduced. Across the test set, anomalies were detected on average 7.4 s after malfunction initiation, with higher severity faults identified more quickly. Window size affected performance: shorter sequences (10 s) produced earlier detection but were also more sensitive to noise and false positives, while longer sequences (20 s) provided stability at the cost of timeliness. Threshold selection strongly affected sensitivity; tighter thresholds improved responsiveness but increased false positives.
The LSTM-Softmax classifier, trained on 60-s transients (trimmed to 10, 30, and 60 s variants), accurately distinguished among six malfunction types. Accuracy improved with longer sequences, though acceptable performance was maintained even with 10 s inputs. Performance was robust across the tested severity range (0.1%–50%). However, because the model was trained exclusively on malfunction data, it always produced a fault label and could not discriminate between nominal and faulty operation.
The combined detector–classifier pipeline demonstrated complementary capabilities. The unsupervised detector enabled timely identification of deviations without relying on labeled fault data, while the supervised classifier provided fault-type specificity once an anomaly was detected. Together, they reduced dependence on large, labeled datasets while mitigating the limitations inherent to each model when used in isolation. Nonetheless, several limitations emerged. Detection timing and false positive rates were highly sensitive to threshold choice, underscoring the importance of systematic threshold calibration. Classifier performance was constrained by the representativeness of simulated faults and was limited in its ability to generalize to unmodeled operational variability. Moreover, the reliance on simulated data restricts the ability to generalize these conclusions to real plant environments without further experimental validation.
4.2 PWR reactor coolant pump thermal barrier leakage
In collaboration with the NRC, Idaho National Laboratory (INL) has looked into the feasibility of using DTs that leverage AI/ML for condition monitoring of NPP components. More than just anomaly detection and classification, this work has investigated the use of AI/ML technologies to quantify the extent of an anomaly, focusing on a reactor coolant pump use case employing INL’s Generic Pressurized Water Reactor (GPWR) simulator (
The GPWR has been benchmarked to an existing ∼1 GWe Westinghouse-type NPP, allowing primary, secondary, and auxiliary systems to be modeled with high fidelity (
The GPWR has built-in “malfunctions” to simulate degradations in the RCP, such as RCP trips due to bus differential, overcurrent and undervoltage locked motor, shaft break, vibration trip due to abnormal vibration readings, thermal barrier leak, seal failure, and oil leak (
4.2.1 Simulation conditions
Simulations were conducted with GPWR to generate plant-realistic time-series data for condition monitoring studies (
The leak scenario progressed from small to severe regimes: steady holds (≤5 gpm), ramps/holds at 10 gpm, and a terminal ramp to 50 gpm (end of simulation), as shown in Figure 4. These sequences were executed under each initial condition.
FIGURE 4

GPWR leak profile used for thermal barrier leakage (
Finally, interpretation of leak magnitudes and alarm-response logic was tied to operator-relevant thresholds from AP1000 Standard Technical Specifications (NUREG-2194), emphasizing ≤10 gpm identified leakage for early detection and response (
4.2.2 Framework for predictive model
To evaluate the feasibility of AI/ML approaches for reactor coolant pump (RCP) degradation, this study applied multiple machine learning models to thermal-barrier leakage scenarios simulated with GPWR. The models addressed two complementary tasks: (1) detection of onset of reactor coolant pump leakage as well as (2) quantifying its severity. A fully connected neural network (FCNN) was adopted as the primary architecture. The network was configured with 53 input variables drawn from plant signals and a single output corresponding to leakage rate, with the overall architecture depicted in Figure 5. To ensure generalizability, the dataset was partitioned into training (35%), validation (35%), and test subsets (30%), and a robust 5 × 2 nested cross-validation strategy was applied, where the outer loop performed 5-fold cross-validation and the inner loop was used for hyperparameter tuning with a 2-fold cross-validation. This nested design reduced bias from single splits and provided a reliable estimate of model performance across diverse operating conditions.
FIGURE 5

Generic architecture of FCNN (
Baseline models—including linear regression and support vector regression—were also tested, allowing for performance comparisons against the FCNN. Evaluation was conducted using standard regression metrics such as RMSE, MSE, and R2, applied consistently across datasets representing BOL, MOL, and EOL reactor states with leakage ranges up to 5 gpm and 50 gpm. Results indicated that the FCNN consistently outperformed baseline models, capturing nonlinear relationships that were especially important for modeling severity in the 5–50 gpm regime. While simpler models retained some predictive value in the very small-leak regime (≤5 gpm), they failed to generalize well to higher leakage magnitudes, underscoring the advantages of more expressive nonlinear models for these types of applications.
Taken together, this structured training, validation, and benchmarking process demonstrated both the feasibility and the limitations of different AI/ML methods for condition monitoring of RCPs. The results highlighted how neural networks can extend beyond anomaly detection to provide robust estimates of degradation severity under variable operating states. Simultaneously, the findings underscored the value of lightweight baseline models as interpretable or redundant safeguards within a broader ACM framework (
4.2.3 Assessment of model performance
To determine the effectiveness of the trained models, performance was assessed through two complementary studies. The first evaluated how well the models captured anomaly onset and degradation progression under simulated operational scenarios. The second quantified predictive uncertainty to measure confidence in early detection and severity estimation. These evaluations highlighted both the strengths and limitations of the models when applied to realistic nuclear plant conditions.
4.2.3.1 Model application to operational scenarios
After benchmarking multiple algorithms for leakage rate estimation across BOL, MOL, and EOL datasets—covering both the small-leak (≤5 gpm) and larger-leak (5–50 gpm) regimes—the authors then applied the trained models to continuous GPWR simulation sequences. The goal was to demonstrate their operational utility by testing whether the models could detect the onset of leakage and accurately track its severity as it evolved over time. The fully connected neural network (FCNN) closely tracked simulator outputs across beginning, middle, and end-of-life reactor states, as shown in Figure 6, which shows predicted and simulated leakage trajectories over the full progression up to 50 gpm. The results indicated that the FCNN could reliably capture the transition from nominal operation to leakage, outperforming simpler regression-based baselines that failed to capture the same non-linear behavior.
FIGURE 6

Comparison between GPWR simulation and FCNN model prediction for BOL test dataset up to 50 gpm (
The models were also applied to quantify the severity and time evolution of degradation, tracking leakage progression up to 50 gpm. Using Figure 6 to highlight both onset detection and progression, the analysis demonstrates how a single trajectory captures the model’s performance in identifying the initial departure from healthy conditions and following the nonlinear growth of leakage. The FCNN reproduced simulator trajectories more accurately than linear or support vector methods, particularly in the higher-leakage regime where nonlinearities dominate. These mentioned demonstrations underscore the feasibility of using machine learning not only for early anomaly detection but also for characterizing degradation severity over time.
Collectively, the applications from this study show how models validated through statistical benchmarking can be leveraged to support monitoring tasks central to nuclear oversight. Figure 6 therefore serves as a representative illustration of both early detection and severity quantification, bridging the two main applications into a single example. By bridging detection with severity quantification, the work illustrates how AI/ML can transition from abstract performance metrics to actionable insights within digital-twin environments, offering a potential pathway for integration into in-service testing programs.
4.2.3.2 Uncertainty quantification for onset detection and severity prediction
To evaluate confidence in early fault identification, the authors applied Monte Carlo–based uncertainty quantification (UQ) to leakage rate predictions in the small-leak regime (≤5 gpm). Results showed (see Figure 7) that predictive uncertainty was lowest at very small leakage values but widened as the leak approached the 5 gpm threshold, reflecting the challenge of distinguishing subtle degradation from nominal variability. The FCNN captured onset transitions while uncertainty bands expanded near threshold values, emphasizing the need for conservative interpretation in operational contexts.
FIGURE 7

Sample result of UQ Analysis: UQ for EOL test dataset up to 5 gpm (
The same UQ framework was applied to leakage progression in the 5–50 gpm regime. Prediction bounds were wider in BOL and MOL phases, reflecting variability during transitions, while the EOL phase exhibited narrower, more stable confidence intervals and lower errors overall, reflecting greater accuracy once degradation was pronounced. Figure 8 illustrates how prediction accuracy was maintained across the full degradation trajectory, while occasional error peaks at rapid transitions or high leakage magnitudes highlighted sensitivity to data scarcity. These findings, supported by summary statistics in Table 1, demonstrate the importance of explicitly quantifying uncertainty for severity estimates to ensure that monitoring outcomes remain regulatorily credible across different operating states.
FIGURE 8

Sample result of UQ Analysis: UQ for EOL test dataset up to 50 gpm (
TABLE 1
| Model | MAE (gpm) | RMSE (gpm) | Averaged uncertainty (gpm) |
|---|---|---|---|
| BOL | 1.19E-01 | 1.88E-01 | 2.84E-01 |
| MOL | 9.60E-02 | 1.60E-01 | 2.45E-01 |
| EOL | 1.61E-01 | 2.46E-01 | 2.63E-01 |
Summary of UQ analysis for the dataset up to 50 gpm (
4.3 Characterizing nuclear cybersecurity states using machine learning
In collaboration with the NRC, Purdue University has looked into the feasibility of using machine learning (ML) technologies for characterizing the cybersecurity states of nuclear plants (
This work used real plant data to construct cases representing plant states resulting from normal operations, abnormal events, and cyber attacks with a goal of identifying technologies that support event differentiation, flexibility of application, and practical measurement within typical licensee constraints of time and resources. Use cases were selected to leverage nuclear and cyber domain knowledge, manifestations of physical impacts, and available operational technology (OT) and information technology (IT) system data. A key goal of this work was to investigate if IT and OT data, typically collected separately, could be leveraged in novel ways to characterize plant normal and abnormal states, and to differentiate cyber attacks resulting in abnormal plant states.
4.3.1 Data collection and represented states
Data collection was facilitated by Purdue’s first-in-the-nation all digital research reactor, PUR-1, which is a pool-type research reactor with a fully digital instrumentation and control system that allows for remote monitoring and the collection of more than 2,000 parameters. Of these available parameters, researchers selected 67 OT and 11 IT parameters as key to state characterization. Using this system, over 20 million data points were collected from both OT and IT systems and used to create data sets representative of 14 plant states. The researchers selected these 14 states to balance research utility with feasibility, e.g., states that would facilitate exploration of interesting research questions within the limits of project budget and time. States represented included normal operation, loss of the plant trip system due to various individual and combined cyber attacks, and loss of the plant trip system from causes other than cyber attacks (Figure 9). Cyber attacks included false data injection (FDI) and Denial of Service (DOS).
FIGURE 9

Representation of nuclear system states, including normal operation, abnormal conditions, and varying levels of DoS and FDI (
4.3.2 Algorithm selection and model development
After the use case was implemented and representative state data was developed, several ML algorithms were selected and evaluated to provide a comprehensive understanding of their limitations and performance-affecting variables. The implementation and performance evaluation of ML algorithms included the design and development of a dedicated classifier architecture, referred to as the composite classifier, consisting of a Boolean combination of three binary classifiers, each with a different classification objective (Figure 10).
FIGURE 10

Composite classifier architecture combining multiple binary classifiers for multi-state characterization of nuclear cybersecurity events (
An extensive search over a broad range of parameters was performed to identify the optimal set of performance-affecting variables. These include window length, window step, training balance ratio, test/validation/train split, and scaling, as well as the best performing ML model developed among the five selected algorithms (Random Forest, Decision Tree, Support Vector Machines (SVM), Logistic Regression, and Naïve Bayes).
4.3.3 Assessment of model performance
Overall, Random Forest models outperformed all other models. It was shown that the Random Forest models were very robust against various balance ratios and window lengths, with only minimal changes in performance when tested with different values for those variables. For these reasons, Random Forest was selected as the best algorithm to use for characterizing cyber events using a classifier trained with separate OT and IT datasets and with combined OT and IT datasets. A significant advantage of Random Forest was its explainability. The high dimensionality and dynamic nature of the problem space makes visualization of the data difficult, and by analyzing the Random Forest model’s structure, researchers were able to identify several erroneous models as well as the signals that introduced incorrect model behavior. This type of model explainability is not currently feasible with SVM, Logistic Regression, Naïve Bayes, or others explored by this project (
The composite classifier approach was tested for this project and showed improved performance with minimal misclassifications when compared with the individual binary classifiers of Levels 1, 2, and 3 alone. This approach demonstrates that multi-state classification of normal, abnormal, and cyber attack events can be achieved by combining multiple simpler binary classifiers within a composite multi-layer architecture, and such an approach can potentially outperform the individual classifiers alone. Because the composite classifier uses combined smaller models, it also enables simplified troubleshooting and updates to individual models within the overall classifier structure (
4.4 Neural operator-enabled virtual sensing-enabled digital twin framework
Researchers at the University of Illinois Urbana-Champaign (UIUC) and New York University (NYU) demonstrated how virtual sensors powered by Deep Operator Networks (DeepONet)-type network can be embedded within DT frameworks for nuclear systems (
In its original form, DeepONet consists of two components: a branch network that encodes input functions such as inlet velocity and a trunk network that processes the spatial coordinates of the output domain. These two outputs are combined through element-wise multiplication to approximate the target solution field. In this application, the branch network processed average inlet velocity (derived from existing physical sensors), while the trunk network handled spatial coordinates corresponding to virtual sensor points within the pipe cross-section.
To overcome these gaps, the researchers trained DeepONet models on high-fidelity ANSYS Fluent CFD simulations of an AP1000 hot leg, using CFD as the ground truth for complex thermal-hydraulic phenomena such as pressure distributions, velocity fields, and turbulence. By learning these relationships, DeepONet can act as a virtual sensor, providing near real-time predictions of system-wide conditions that are otherwise impractical to measure directly. Importantly, the approach delivers orders-of-magnitude faster inference than CFD while maintaining strong agreement with its outputs, highlighting a path toward continuous observability without the prohibitive cost of constant simulation.
From a broader perspective, this study illustrates how CFD and AI can be coupled within DT frameworks: CFD provides validated physics-based data, and DeepONet accelerates its use for real-time monitoring. This synergy underscores the potential of DTs to reduce reliance on costly outages and enable predictive, condition-based strategies for reactor monitoring and maintenance.
4.4.1 DeepONet as a digital twin framework
The DeepONet developed in this study (
) functions as a digital twin for plant operations, consistent with the U.S. Nuclear Regulatory Commission’s definition of a digital twin. Its architecture supports real-time predictive capability, continuous synchronization with plant conditions, and adaptability to evolving operational states.
Dynamic Representation and Synchronization with the Physical System: DeepONet provides a live, computational mirror of the physical system by generating instantaneous predictions of system behavior. A core requirement of digital twin technology is the ability to remain synchronized with the physical asset. DeepONet satisfies this requirement by ingesting real-time signals through a supporting data pipeline and updating its predictions accordingly. The model can be trained using high-fidelity simulation data, as done with the ANSYS datasets in this study, and subsequently refined using operational measurements, allowing it to evolve in parallel with the physical system.
In this framework, the branch network processes real-time inlet measurements, while the trunk network resolves spatial fields throughout the domain, effectively acting as a virtual sensor array. This enables DeepONet to augment sparse physical instrumentation by providing full-field estimates of parameters such as velocity, pressure, and turbulence in regions where direct measurement is infeasible. The strong agreement between DeepONet predictions and CFD ground truth demonstrates its ability to reliably reproduce system behavior, establishing it as a robust digital surrogate for plant monitoring.
Real-Time Inference: A defining feature of a digital twin is its ability to deliver actionable insights at operational timescales. DeepONet achieves this through extremely fast inference, roughly three orders of magnitude faster than conventional finite-volume simulations. This performance allows operators to monitor key thermal-hydraulic quantities nearly instantaneously, supporting timely decision-making in environments where rapid assessments are critical.
Adaptability to Changing Operating Conditions: Digital twins must remain valid across a range of operating conditions and must not require constant retraining. DeepONet meets this requirement by learning the underlying operator that maps inlet conditions to spatial fields, enabling it to generalize across diverse flow regimes. The network maintains high predictive fidelity under varied inlet states and accurately reconstructs pressure, velocity, and turbulence distributions without retraining. This resilience to operating-condition changes aligns with the NRC’s emphasis on adaptive, synchronized, and continuously representative digital twin models.
4.4.2 Simulation conditions
Virtual sensors are software-based models that replicate the function of physical sensors by estimating key system parameters from available data rather than direct measurement. Unlike physical instrumentation, virtual sensors can provide insight into regions that are inaccessible, too harsh for instrumentation, or impractical to monitor continuously. Within a DT framework, they complement sparse physical sensor networks, effectively filling in coverage gaps to generate a more complete picture of reactor conditions.
To enable development of virtual sensors, the researchers selected the AP1000 hot leg as a representative case study and conducted high-fidelity CFD simulations to generate training datasets under representative operating conditions. This section of primary piping, which carries high-pressure, high-temperature coolant from the reactor vessel to the steam generator, is both critical for safety and particularly challenging to instrument due to extreme operating conditions and geometric complexity. Because simulating the full-scale geometry was computationally prohibitive, the team employed geometric scaling: the hot leg pipe diameter (≈787 mm) was reduced to 25 mm, and the flow length was scaled to 150 mm, while maintaining dynamic similarity through Reynolds number matching. This ensured that turbulent flow features such as recirculation, separation, and pressure gradients were realistically preserved in the scaled CFD model. The geometry of the hot leg was therefore essential not only for creating the CFD training dataset, but also for defining the spatial coordinate system in which virtual sensors operate. The dataset was normalized using min–max scaling to ensure consistent parameter ranges and then divided into training and testing subsets (80%–20%), with cross-validation applied to assess model generalization.
4.4.3 Neural operator-based digital twins for real-time inference with minimal retraining
Operational shifts cause a dataset shift, which forces continual AI/ML retraining that is infeasible for real-time digital twins in nuclear plants. The modeling approach centered DeepONet learns the underlying solution operator over the operating envelope, eliminates frequent retraining, and delivers fast, accurate inference for new conditions, enabling real-time DT capability (
To improve predictive performance, the authors extended this baseline structure by adding parameter-specific linear layers after the combined representation, enabling separate refinement of pressure, velocity, and turbulence predictions. The resulting modified architecture is shown in Figure 11, which highlights the original DeepONet components on the left and the additional output-specific layers on the right.
FIGURE 11

Modified DeepONet architecture for AP1000 hot leg virtual sensing. Left-hand portion (branch + trunk networks with element-wise multiplication) corresponds to the original DeepONet, which directly outputs solution fields. The modified architecture extends this baseline by adding parameter-specific linear layers (right), enabling separate refinement of velocity, turbulence kinetic energy, and pressure predictions (
The authors evaluated both the original DeepONet and the modified version. Model training involved Bayesian hyperparameter optimization using the Optuna framework, with mean squared error (MSE) as the loss function and the Adam optimizer with L2 regularization to prevent overfitting. Training was conducted using early stopping and 5-fold cross-validation to balance accuracy and efficiency. Once trained, the DeepONet model was compared against the original DeepONet architecture and evaluated across multiple train-test splits and mesh resolutions to assess robustness. Another study also shows DeepONets’ feasibility in solving the bottleneck of real-time prediction capabilities for nuclear digital twin systems (
By coupling CFD-derived datasets with DeepONet, this study shows how virtual sensors can provide near-real-time insights into hot leg behavior, illustrating a possibility toward predictive IST practices and demonstrating the broader role of DTs in modernizing reactor monitoring.
4.4.4 Assessment of model performance
The study showed that DeepONet-based virtual sensors can predict thermal-hydraulic conditions in the AP1000 hot leg with high accuracy and efficiency, offering a viable alternative to CFD for real-time monitoring. Compared with the original DeepONet architecture, the modified model used in this study with parameter-specific linear layers achieved better performance across all quantities of interest. Pressure fields were captured with the greatest fidelity (MSE ≈2.6 × 10−4, Relative L2 ≈ 2.0%), velocity predictions were moderately accurate (Relative L2 ≈ 5.1%), and turbulence proved most challenging (Relative L2 ≈ 10.3%), underscoring the difficulty of resolving high-frequency flow structures in data-driven models. Representative velocity predictions across best- and worst-case scenarios are illustrated in Figure 12, which serves as an example of the broader performance trends reported in the original study.
FIGURE 12

Comparison of CFD simulations with DeepONet velocity predictions for the AP1000 hot leg in representative cases [best (a–c), 25th percentile (d–f), 50th percentile (g–i), 75th percentile (j–l), and worst (m–o)]: ANSYS ground-truth CFD results (left), DeepONet predictions (middle), DeepONet error distribution Q9 (right) (
Robustness tests further validated the model. Performance was stable across different train–test splits (70%–30%, 80%–20%, 90%–10%), indicating that the network generalized well to unseen data. Similarly, reducing the number of spatial nodes by three-fourths had little impact on prediction quality, suggesting that the approach remains effective even with reduced resolution or sparser data availability. This flexibility is important for real-world implementation, where sensor placement and computational resources are often constrained.
Equally significant is the computational gain. Once trained, the DeepONet produced predictions in 0.135 s compared to nearly 200 s for a single CFD simulation, an improvement by a factor of about 1,500. This speed advantage enables continuous monitoring within a DT framework, meeting a fundamental requirement for supporting IST activities in real time.
An analysis of error distributions revealed clear patterns. Pressure was predicted most consistently, with tight error bands across the test set. Velocity predictions exhibited greater variability in regions with strong gradients, such as near the elbow, where flow separation is common. Turbulence was the least accurate, particularly in low-magnitude regions where the model smoothed out small-scale fluctuations. These limitations reflect the well-known spectral bias of neural networks, which favor capturing large-scale, low-frequency features.
Taken together, the findings demonstrate that DeepONet virtual sensors can extend the reach of physical sensor networks, providing accurate and high-frequency predictions of critical parameters in harsh environments and geometrically complex locations where direct measurement is not feasible. While turbulence remains a challenge, the demonstrated balance of accuracy, robustness, and computational efficiency highlights the potential of virtual sensing to advance IST within a digital twin environment.
5 Explainability and trust in AI/ML-enabled digital twins
The integration of AI/ML into DTs for nuclear applications raises important questions of explainability and trust. While predictive accuracy is necessary, regulatory and industry stakeholders must also be able to interpret model behavior and understand the basis of predictions. This requirement stems from the high-consequence nature of nuclear safety decisions, where a lack of transparency may undermine operator confidence or complicate regulatory acceptance.
Explainability methods, such as Local Interpretable Model-Agnostic Explanations (lime), have been demonstrated in ACM use cases to highlight which input features most strongly influence predicted outcomes. The work of Godbole et al. showed how, in RCP degradation scenarios, these tools revealed that cooling water return flow strongly influenced predictions of leakage rates across different core-life phases (
Trust is further reinforced by combining explainability with rigorous verification, validation, and uncertainty quantification (VVUQ). Model predictions must be framed within known confidence bounds and linked to physically meaningful parameters, ensuring that AI/ML tools complement—rather than obscure—engineering judgment. As emphasized in both nuclear applications and broader safety-critical domains, explainability also facilitates human–machine teaming by enabling plant staff to trace why an alert was generated and whether corrective action is warranted (
Ultimately, explainability and trustworthiness are prerequisites for the deployment of AI/ML-enabled DTs in nuclear condition monitoring. Methods that provide interpretable, physics-informed explanations alongside predictive outputs will be essential to achieving regulatory consideration.
6 Implications and moving forward
The work of Villarreal et al. demonstrated that machine learning–based anomaly detection and classification can strengthen condition monitoring of BWR recirculation pumps by enabling timely detection of abnormal behavior and subsequent fault identification (
The work of Godbole et al. highlighted how AI/ML-enabled condition monitoring can provide key building blocks for DTs in nuclear systems (
The work of Hossain et al. demonstrated the use of DeepONet-based virtual sensors to extend observability in nuclear systems where direct instrumentation is impractical. Using CFD-derived datasets of the AP1000 hot leg, they trained a modified DeepONet architecture with parameter-specific linear layers to predict pressure, velocity, and turbulence with high accuracy (
The work of Chatzidakis et al. highlighted several issues directly applicable to nuclear DTs. First, adequately identifying key plant components and states to be modeled is critical, followed by collecting data that sufficiently characterizes those components and states (
Taken together, these studies illustrate how AI/ML-enabled condition monitoring and DTs can shift nuclear IST and ISI practices from interval-based compliance toward predictive, risk-informed frameworks. By coupling high-fidelity physics (e.g., CFD) with scalable learning architectures (e.g., DeepONet) and integrating uncertainty quantification, DTs can provide regulatorily credible evidence of ongoing system health while reducing outage costs and surveillance burden. The reviewed work highlights a convergence of methods—anomaly detection, uncertainty-aware diagnostics, and virtual sensing—that collectively strengthen observability and trustworthiness. Equally significant, explainability is essential for regulatory and operational acceptance. Interpretable models ensure that predictions are not only accurate but also understandable, providing operators and regulators with the transparency needed to act confidently on AI/ML-driven insights. Embedding explainability directly within DT frameworks will be critical to closing the gap between technical feasibility and regulatory alignment, ensuring that future IST and ISI practices can be trusted. The future of IST and ISI with DTs depends on making these technologies not only predictive, but also explainable and trustworthy.
Statements
Author contributions
HM: Data curation, Formal Analysis, Investigation, Methodology, Validation, Visualization, Writing – original draft, Writing – review and editing. VY: Conceptualization, Data curation, Investigation, Methodology, Validation, Visualization, Writing – original draft, Writing – review and editing. SA: Conceptualization, Investigation, Methodology, Validation, Writing – original draft, Writing – review and editing. DE: Conceptualization, Methodology, Validation, Writing – original draft, Writing – review and editing. RI: Conceptualization, Methodology, Project administration, Supervision, Validation, Writing – original draft, Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This manuscript was completed as part of the authors’ professional roles but received no dedicated funding. The various works reviewed for the manuscript were supported through various sources that include the U.S. NRC, the National Science Foundation, and the United States Department of Energy.
Acknowledgments
The authors acknowledge the many investigators whose original studies provided the foundation for this review and thank them for their contributions to advancing the field.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
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Summary
Keywords
artificial intelligence, condition monitoring, digital twins, inservice inspection, inservice testing, machine learning, nuclear energy, virtual sensing
Citation
Mendoza H, Yadav V, Alam SB, Eskins D and Iyengar R (2026) Advances in digital twins and AI/ML for condition monitoring in nuclear applications. Front. Energy Res. 14:1716514. doi: 10.3389/fenrg.2026.1716514
Received
30 September 2025
Revised
17 December 2025
Accepted
16 January 2026
Published
18 February 2026
Volume
14 - 2026
Edited by
Stylianos Chatzidakis, Purdue University, United States
Reviewed by
Keyou Mao, Florida State University, United States
Luis Rojas Valdivia, Pontificia Universidad Católica de Valparaíso, Chile
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Copyright
© 2026 Mendoza, Yadav, Alam, Eskins and Iyengar.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Raj Iyengar, raj.iyengar@nrc.gov
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.