The PUR-1 Cyber-Physical Digital Twin

1 Introduction

• Digital I&C, sensors, and remote monitoring could improve nuclear flexibility, but reactor complexity, sparse in-core measurements, communication latency, and safety constraints impede their use without an integration framework.The introduction frames digital twins as a way to integrate real-time operational data with computational models.Source: §1 · p. 2
• DTs exchange data bidirectionally with physical assets, infer unmeasured states in forward problems, and derive control strategies in inverse problems.These capabilities can extend observability, support predictive maintenance, and aid real-time operator decisions.Source: §1 · p. 2
• Nuclear DT applications remain nascent, with many efforts conceptual, fragmented, or limited to non-nuclear test environments and only a few validated in operating reactors.The introduction surveys laboratory, industry, and academic initiatives while identifying the need for operating-reactor validation.Source: §1 · p. 2
• The PUR-1 DT couples multiphysics forward models, inverse optimization, and machine-learning surrogates with bilateral communication to synchronize with reactor operations.PUR-1 is described as the first U.S.-licensed reactor with a fully digital I&C system, making it a testbed for the DT.Source: §1 · pp. 2–3
• The work defines nuclear DT requirements and demonstrates real-time synchronization, state estimation, anomaly detection, and forecasting, alongside model benchmarking and full-cycle accuracy and latency assessment.The benchmarking covers neutronics, thermal-hydraulics, and ML-based surrogate models; filtering and surrogates are trained on high-fidelity simulations.Source: §1 · p. 3

2.1 Definitions

• A digital twin is an evolving, high-fidelity representation of a physical asset with dynamic exchange, while integration ranges from static models through one-way shadows to bidirectionally coupled twins.Core properties also include real- or near-real-time synchronization, sufficient model fidelity, and adaptability as the physical system evolves.Source: §2.1 · pp. 3–4, Figure 1 · p. 5

2.2 Digital Twin for Nuclear Environment Applications

• Nuclear reactor digital twins require real-time, synchronized, bidirectional operation that supports state estimation, forecasting, decision support, predictive control, and anomaly detection.Additional requirements include short- and long-term hidden-state forecasting; high-fidelity three-dimensional neutron-flux, temperature, and flow reconstruction; accuracy above 90%; explainability and uncertainty quantification; maintainability, user-facing AI/AR/VR, and cybersecurity.Source: §2.2 · p. 5

2.2.1 Related Work

• Academic reactor digital-twin work often lacks real-time operational data; limited examples include near-real-time AGN-201 twinning and non-synchronized, one-way research-reactor shadows.Nuclear efforts also include NRIC, MAGNET, and VERA initiatives,,, while Exelon and Framatome/EDF explore incident analysis and operator training,.Source: §2.2.1 · p. 6

3.1 Design Approach

• Nuclear-reactor DT design links system characteristics and requirements to architectural capabilities through a traceable, requirement-driven process.Design must account for model fidelity, data availability, reactor dynamics, latency, uncertainty, and cybersecurity.Source: §3.1 · pp. 6–7, §3 · p. 6

3.2 Development Process

• Conceptual development defines system boundaries, functions, information flows, state variables, data needs, fidelity, prediction horizons, acceptance criteria, and modeling approach.Physics-based, data-driven, and hybrid methods offer different tradeoffs; the choice should follow DT process requirements.Source: §3.2 · pp. 7–8
• Preliminary development decomposes the architecture into models, processes, and interfaces, develops and evaluates components, and verifies their accuracy, stability, and uncertainty.High-fidelity models can provide reference solutions and training data; reduced-order or surrogate models can help meet synchronization needs when execution is too slow.Source: §3.2 · p. 9
• Final development integrates validated components and tests end-to-end synchronization, latency, robustness, uncertainty propagation, cybersecurity overhead, and human–system interaction against design criteria.Integration coordinates data dependencies, communication paths, execution order, update frequencies, and consistency between component inputs and outputs.Source: §3.2 · p. 9

3.3 Operational Framework

• During operation, the DT assimilates reactor measurements into an updated digital state, uses it for estimation, forecasting, anomaly detection, and decision support, and may return outputs through bidirectional control.A layered workflow acquires and post-processes observations, models and simulates state reconstruction and prediction, and presents outputs to users; critical processes remain synchronized despite differing update frequencies.Source: §3.3 · p. 9, Figure 2 · p. 10

• PUR-1 measurements continuously update the virtual asset, while DT-generated actions are evaluated through an independent actuation pathway to enable bidirectional interaction.The operational cycle was identified to select a modeling strategy balancing accuracy with available computational resources.Source: §4 · p. 10
• Dedicated estimation, prediction, AI/ML, PID, and MPC–MHE modules support state estimation, forecasting, anomaly detection, and predictive control within reactor safety-system bounds.Source: §4 · p. 10
• High-fidelity neutronic and thermal-hydraulic models reproduce detailed reactor geometry and unobserved physical phenomena; individual benchmarking, uncertainty quantification, and alternative models address accuracy, explainability, and confidence.The selected approach targeted above 90% overall accuracy, a 10 s forecasting horizon, and monitoring of at least 5 concurrent signals.Source: §4 · p. 10
• A maintainable, adaptable user interface supports user–system interaction, while the communication architecture accommodates authentication, encryption, and QKD-assisted cryptographic schemes without compromising synchronization.Source: §4 · p. 10

5 PUR-1 DT Configuration

• The reactor supplies real-time measurements through a unidirectional pathway, while CERVEROS adds sensing and bidirectional actuation; DT control commands return only to CERVEROS.Data from both subsystems update the virtual asset, preserving isolation of the PUR-1 control system.Source: §5 · p. 10
• The integrated DT combines live measurements, testbed data, physics and surrogate models, AI/ML diagnostics, and visualization to support state awareness, field estimation, prediction, scenario evaluation, and anomaly detection.Reactor conditions can be visualized through graphical and augmented-reality interfaces.Source: §5 · p. 11
• Figure 3 depicts the synchronized architecture linking physical subsystems with data processing, modeling, surrogate models, visualization, and action evaluation.The architecture combines physical and virtual components into a real-time decision-support environment rather than a standalone simulation tool.Source: §5 · p. 11, Figure 3 · p. 11

6.1 Purdue University Reactor One (PUR-1)

• PUR-1 is a naturally circulated, light-water-moderated non-power reactor with 16 HALEU fuel elements, three control rods, and graphite reflectors; graphite assemblies enable capsule irradiation experiments.It is the first U.S. reactor licensed by the NRC to operate with a fully digital I&C system and serves education and research applications.Source: §6.1 · p. 12

6.2 Cyber-Physical Testbed (CERVEROS)

• Installed in the reactor pool, CERVEROS operates independently of reactor I&C while enabling bilateral communication and evaluation of DT-originated actions.Its instrumentation includes temperature sensors, and its AMDR provides a mechanism for inserting external perturbations by emulating control-rod movements.Source: §6.2 · pp. 12–13
• CERVEROS uses an actuator-driven Auxiliary Moderator Displacement Rod to perturb neutron population through moderator displacement, with effects observable by existing neutron detectors.The AMDR comprises indium foils in a sealed plastic container mounted on an aluminum extension.Source: §6.2 · p. 13
• AMDR reactivity worth is calculated from reactor period using the In-hour equation, with neutron-flux change measured before and after small rod movements while the reactor remains critical.Operators apply compensatory actions to offset the AMDR-induced reactivity perturbation; the worth curve is evaluated as a function of AMDR position,,.Source: §6.2 · pp. 13–14
• The two-term sinusoidal fit to AMDR reactivity-worth data lies within experimental uncertainty bounds; uncertainty grows above 30 cm as differential worth and neutron-population changes decrease.The larger fractional uncertainty arises because detector uncertainty is approximately constant while the measured response becomes smaller.Source: Figure 7 · p. 14, §6.2 · p. 14

6.3 Data Acquisition System

• PUR-1’s nuclear-grade digital controller monitors and controls more than 2,000 parameters, stores data in real time, and connects directly to sensors to minimize transfer latency; regulatory restrictions impose a data diode.The virtual system must operate at the controller frequency for real-time state awareness and decision support. CERVEROS instead uses an independent architecture with bidirectional OPC UA exchange and supports controlled evaluation of cybersecurity authentication and encryption,.Source: §6.3 · pp. 14–15

7.1 Data layer

• The data layer preprocesses noisy, irregular operational measurements and extracts preliminary anomalies, faults, system states, and key parameters for downstream DT layers.Filtering, interpolation, and classification address artifacts such as outliers and missing values; digital filtering can also support detection of abnormal noise patterns.Source: §7.1 · p. 15

7.2.1 Forward Problem Approach

• With limited sensor coverage, the forward framework couples CFD, Monte Carlo neutron transport, and point kinetics to reconstruct thermal and neutronic fields and resolve reactor transients.CFD estimates component temperatures, heat and coolant-flow distributions, and localized hotspots; OpenMC supplies neutron, gamma, and heating distributions, while power and temperature fields are iteratively coupled. Point kinetics is triggered manually or when measured power ramps exceed 0.5%/s.Source: §7.2.1 · pp. 16–18

7.2.2 Inverse Problem Approach

• The inverse model uses a target reactor state and initial digital state to identify feasible operating trajectories, then ranks them by downstream reactivity or safeguards objectives.Candidate objectives include minimizing reactor poisoning or fuel depletion, extending refueling cycles, and supporting cybersecurity or defense-in-depth.Source: §7.2.2 · pp. 18–19

7.2.3 Anomaly Detection, Explainability, and Control Modules

• Random Forest models distinguish normal, abnormal, and cybersecurity-related events in OT and IT data, while SHAP-based explanations interpret multivariate time-series model outputs.The state-estimation and anomaly-detection modules were evaluated in real operational scenarios and showed high alignment with real data and higher-accuracy virtual-system modules.Source: §7.2.3 · pp. 19, 21
• PID and MPC–MHE controllers use estimated and predicted states to track power demand within reactor limits, while a communication model represents packet loss, latency, and quantization.The DT framework supports evaluation of supervised automated control and progressively autonomous operation strategies.Source: §7.2.3 · pp. 19–22

7.2.4 Forecasting

• Monte Carlo and Multiphysics simulations take 2 hours and 8.6 hours on HPC clusters, respectively, motivating ROMs and SMs to estimate keff and neutron flux for current and future states.Training data are generated by varying control-rod heights in 0.1 cm increments and sweeping reactor power levels and initial conditions.Source: §7.2.4 · pp. 23–24

7.3 Visualization layer

• The visualization layer provides an interactive GUI combining real-time OT data and DT outputs with consequence analysis, recommended actions, and selectable simulation models.Operators can also interact through demonstration-room displays and an augmented-reality environment, while a RAG interface queries curated documentation, historical context, and live data with synchronized responses, source excerpts, and reasoning traces.Source: §7.3 · pp. 24–26

8 Cyber-physical Integration

• A real-time bus and DeepLynx integration route interprocess data directly between DT processes rather than through the cloud server.DeepLynx also consolidates physical and virtual signals with metadata and provenance, while graph-based exploration traces their dependencies through processing, estimation, modeling, and visualization.Source: §8 · p. 27
• Data adapters before each process refine, validate, and standardize inputs, while surrogate models reduce the runtime burden of high-fidelity simulations.The adapters are Python-based and address errors from inconsistent formats or abnormal data characteristics.Source: §8 · p. 28

8.1 Network Communications

• The architecture uses UDP from the RTP 3000 TAS controller to the historian, TCP/IP from the historian to the virtual system, and OPC UA for bidirectional exchange with the CERVEROS testbed.The OPC UA server on the Schneider Modicon M241 PLC exposes selected measurements and receives authorized AMDR commands; the links can use symmetric encryption with QKD-generated keys, with encrypted data carried over authenticated classical channels.Source: §8.1 · p. 28
• Approximately 390 ms mean latency was measured for transmitting up to 2,000 reactor signals across the evaluated OTP, AES-256, and ASCON configurations.The reported latency covers communication and cryptographic operations; model-execution time is evaluated separately. The authors report that secure communication can be incorporated without disrupting real-time data availability.Source: §8.1 · pp. 28–29, Figure 25 · p. 29

8.2 Internal Communication Latency Analysis

• Internal latency analysis tracks module execution time and presentation time, with synchronization maintained when the relevant end-to-end latency is below 1 second.Execution latency follows the computational dependency path: sequential workflows sum participating module times, while parallel workflows are governed by the longest dependent path. Presentation delay is negligible for scalar values and alerts but can be significant for rendered three-dimensional fields, depending on resolution, mesh density, and workstation resources.Source: §8.2 · pp. 29–30

9.1 Monte Carlo Benchmarking

• 6.75% average deviation separated simulated from experimentally calculated total neutron flux, falling to 2.89% at medium- and high-flux positions, with lower correlation at low flux.The OpenMC benchmark used more than 60 gold foils irradiated at axial and radial core-boundary locations, with flux derived through neutron activation analysis.Source: §9.1 · pp. 30, 32, Figure 27 · p. 33

9.2 Multiphysics Benchmarking

• 1.37% average percentage difference was found between COMSOL pool-temperature simulations and experimental data using 153 points within 20 inches of the pool surface.Simulation outputs were extracted every 15 minutes over the same five-hour span and power inputs as the experimental study.Source: §9.2 · p. 33, Figure 28 · p. 34

9.3 Point Kinetics Equations

• 6.89% average percentage difference between point-kinetics predictions and measured neutron population was found across offline historical scenarios from startup to shutdown.The model includes six delayed-neutron groups with parameters obtained from OpenMC; forecasting was not activated for this offline comparison.Source: §9.3 · pp. 34–35

9.4 Effective Multiplication Factor Prediction

• The control-rod-height surrogate predicts effective multiplication factor, and the radial basis function kernel achieved the lowest RMSE and was selected as PUR-1 DT’s default model.Kernel selection considered accuracy, goodness-of-fit, and training and tuning time; uncertainty estimates support prediction confidence and scenario-specific model selection.Source: §9.4 · pp. 35–36, Table VII · p. 37

9.5 Neutron Flux Field Prediction

• 3.62% average percentage difference across the full neutron flux field and 17.81% average percentage error against experimental gold-foil flux were reported for the flux-field surrogate.Maximum local discrepancies reached 70%, concentrated near control rods, the source assembly, and field boundaries; low reference flux amplified relative error. The model predicts a three-dimensional field from control-rod positions using log-domain target fields.Source: §9.5 · pp. 38–40, Figure 32 · p. 39, Figure 33 · p. 40

Use case

• The workflow was evaluated over two repetitions of a cycle transitioning from 0% to 10%, then 65%, and back to 0% power.PKE, Monte Carlo, and multiphysics simulation models and their corresponding surrogates execute in different orders depending on steady or transient operation.Source: §10 · p. 40, Figure 34 · p. 41
• The integrated estimates provide reactor-pool temperature distributions, core neutron-flux distributions and keff, and real-time inserted reactivity and power from observations and model outputs.The multiphysics model estimates temperature first; component temperatures and control-rod positions then inform the OpenMC-based surrogate, followed by the PKE model.Source: §10 · p. 41
• Figure 35 presents PUR-1 DT power predictions in comparison with power values collected from the reactor instrumentation system.Source: Figure 35 · p. 42
• The keff surrogate remained synchronized with reactor operation, reflecting different control-rod reactivity worths as RR, SS2, and SS1 were used in steady-state, power-change, and startup/shutdown phases, respectively.The core neutron-flux field was continuously reconstructed from control-rod configuration and presented to the operator.Source: §10 · p. 42, Figure 36 · p. 42
• The COMSOL model predicts heat flux and reactor-pool temperature over 300 time steps, using the current reactor state as its initial condition.With an approximately 100 s runtime, it reports effects over the preceding 100 s and projects the state at t_N+200; new operator actions trigger a simulation with updated initial conditions.Source: §10 · pp. 42–43, Figure 37 · p. 43
• All three workflows remained below the 1 s no-delay threshold in the baseline communication configuration, but neutron-flux-field presentation periodically exceeded the 610 ms budget with 390 ms secure-transmission latency.The flux surrogate alone remained below both thresholds; the additional delay came primarily from rendering and displaying the high-resolution 3D field, which could be updated less frequently without delaying model output to other DT processes.Source: §10 · pp. 43–44, Figure 38 · p. 44, Figure 39 · p. 45

11 Lessons Learned

• System-level latency can exceed individual models’ 1 s update intervals because of sequential dependencies, communication, and visualization.The team used surrogates for time-critical processes, critical-path latency analysis, and lower-frequency visualization for computationally intensive outputs.Source: §11 · p. 45
• Uniformly fine meshing was impractical, with runtimes exceeding 28 h per case, so nonuniform refinement near the core reduced computational burden while preserving experimentally observed thermal behavior.The approximately 5 m pool depth and approximately 2 mm fuel-plate thickness contributed to the computational cost.Source: §11 · p. 45
• Optimizing OpenMC batches and particles per batch reduced simulation runtime from approximately 2 h to approximately 18 min per case while preserving Monte Carlo model accuracy.The optimization addressed the cost of generating a 2,500-run training dataset; accuracy gains became marginal beyond a convergence threshold.Source: §11 · p. 45
• A moving-average filter suppressed high-frequency noise in AMDR position data, while repositioning the ultrasonic sensor and target surface minimized interference from nearby objects.The sensor had produced intermittent outliers from reflections within the measurement area.Source: §11 · p. 46
• Models trained on historical or synthetic data may become unreliable as physical conditions evolve, requiring reassessment against operational data and, when needed, recalibration or retraining.Sensor noise, communication disturbances, and operational variability may be insufficiently represented during model development.Source: §11 · p. 46

12 Discussion and Conclusions

• The DT synchronized with PUR-1 at 1 Hz, with deviations below 10% for flux mapping and approximately 2% for thermal fields.Benchmarking used neutron flux distributions from gold foil activation and thermal-hydraulic pool-temperature measurements to verify the Monte Carlo and Multiphysics modules.Source: §12 · p. 46
• DT predictions differed from physical-system measurements by an average of 9.2% across the full operational cycle, supporting state identification, short-term forecasting, and operator decision support.The use case extended observability beyond instrumentation limits and provided predictive insight for enhanced control and more efficient reactor operation.Source: §12 · p. 46
• PKE and neutronic surrogate workflows met the 1 s synchronization requirement including encrypted communication overhead, while high-resolution flux visualization could update asynchronously.Simulation-trained surrogate models enabled real-time prediction of key parameters while preserving physical interpretability and avoiding high-fidelity simulation latency.Source: §12 · p. 46
• Forecasting accuracy remained sensitive to control-rod reactivity-worth uncertainty and sensor artifacts, especially during transients; flux surrogates had localized discrepancies and Multiphysics updated less frequently.The Multiphysics model's lower update frequency reflected its higher computational cost.Source: §12 · p. 46
• The DT provides a reference architecture for nuclear applications, with potential extensions to autonomous control, predictive maintenance, operator training, and smart-grid integration.Continuous data exchange makes robust cybersecurity necessary; anomaly detection and explainable AI were incorporated to mitigate false data injection, but comprehensive defenses against evolving threats remain essential.Source: §12 · pp. 46–47