PaperlayerView exact revision on arXiv

Source-linked AI summary

The PUR-1 Cyber-Physical Digital Twin

Vasileios Theos, Jonah Lau, Konstantinos Gkouliaras, Zachery Dahm, Konstantinos Vasili, Noah Fillgrove, William Richards, True Miller, Brian Jowers, Stylianos Chatzidakis

arXiv:2608.30186v1cs.CEcs.LG

TL;DR

Nuclear digital twins must integrate accurate, explainable models with low-latency, bidirectional synchronization, but reactor physics, sparse measurements, and computational cost make this difficult. The paper develops and experimentally validates the PUR-1 cyber-physical DT using high-fidelity physics models, surrogate models, and real-time communications. It achieves 1 Hz synchronization, with flux-mapping deviations below 10%, thermal-field deviations of approximately 2%, and average predictive differences of 9.2%.

  • Problem

    Nuclear digital twins need synchronized, explainable, multi-model decision support despite reactor-physics complexity, limited measurements, communication latency, and computational delays.

  • Method

    The PUR-1 DT couples high-fidelity neutronics and thermal-hydraulics, surrogate models, real-time data exchange, and cyber-physical testbed integration for estimation, forecasting, diagnostics, and control.

  • Results

    1 Hz synchronization, flux-mapping deviations below 10%, thermal-field deviations of approximately 2%, and an average predictive difference of 9.2% were demonstrated across reactor operation.

  • Takeaways & Limitations

    The validated PUR-1 framework establishes the feasibility of real-time cyber-physical digital twins in research reactors and supports further DT-enabled functionality evaluation.

  • Takeaways & Limitations

    Forecasting remains sensitive to control-rod reactivity uncertainty and sensor artifacts, while localized flux discrepancies, lower Multiphysics update frequency, and evolving cyber threats remain.

Abstract

from arXiv · show

Digital twin technologies have the potential to improve operational flexibility and responsiveness capabilities of nuclear systems. To provide decision support, cyber event characterization, state estimation, predictive control, and real-time dynamic processing of operational data, however, an efficient digital twin needs to integrate multiple models (data-driven as well as physics-based) with explainability while at the same time maintain two-way synchronization with the physical facility at a time constant less than its operational cycle. In this work, we present the Purdue University Reactor One Digital Twin (PUR-1 DT), a cyber-physical digital twin with a complete high-fidelity physics-based and AI-driven virtual model stack (neutronics, thermal-hydraulics, point kinetics) which provides closed-loop explainable diagnostics, forecasting, predictive control, and action recommendation back to the reactor via two-way communications and a cyber-physical testbed. We demonstrate real-time synchronized state estimation and short-term forecasting over a full reactor operational cycle and conduct a series of benchmarking experiments to validate accuracy and latency. Our results show good agreement with experimental results and lay the groundwork for further development and experimental demonstration of DT-enabled functionalities in real-world facilities.

1 Introduction

Nuclear digital twins are motivated by the need for more flexible, responsive reactor operation despite measurement, latency, physics, and safety constraints. The PUR-1 DT addresses this need through real-time cyber-physical integration, multiphysics and machine-learning models, and experimental validation.

  • Nuclear systems face limited operational flexibility, rising operation and maintenance costs, and difficulty adapting to fluctuating energy demand.
  • Complex reactor physics, sparse in-core measurements, communication latency, and stringent safety constraints hinder effective deployment of advanced digital instrumentation and monitoring.
  • Digital twins exchange data bidirectionally with physical assets, enabling hidden-state reconstruction and control-action recommendations through forward and inverse problems.
  • Nuclear digital-twin applications remain relatively nascent despite established tools and frameworks from national laboratories and industry.
  • The paper presents the design, implementation, and experimental validation of a real-time digital twin for Purdue University Reactor One.
  • The PUR-1 DT combines multiphysics models, inverse optimization, and machine-learning surrogate models to synchronize with the reactor cycle and support diagnostics, forecasting, and control.

2 Background

Digital twins are high-fidelity, dynamically evolving representations linked to physical assets through data exchange, but definitions and integration levels vary by application. Nuclear deployments require additional real-time, synchronized, bidirectional, and safety-conscious capabilities.

  • Digital-twin definitions vary in integration level, model fidelity, data integration, and adaptability, but converge on dynamic data exchange with a physical asset.
  • Integration levels range from static digital models, through one-way digital shadows, to bidirectionally coupled digital twins.
  • Core digital-twin properties include bidirectional exchange, real-time or near-real-time synchronization, sufficient physical fidelity, and adaptation with the physical counterpart.
  • Nuclear reactor digital twins additionally require real-time acquisition, dynamic updating, bidirectional communication, operational-cycle synchronization, estimation, forecasting, decision support, and predictive control.
  • Nuclear digital-twin research remains constrained because real-time operational data are often unavailable and implementations frequently use synthetic, simulated, or nonsynchronized datasets.

3 Digital Twin Architecture

The proposed architecture translates nuclear-system requirements into a layered, progressively integrated digital-twin framework. It coordinates data acquisition, validated models, cyber-physical interfaces, and operational feedback for estimation, forecasting, anomaly detection, and decision support.

  • Design Approach: Digital-twin development begins with requirement-driven design that accounts for model fidelity, data availability, reactor dynamics, latency, uncertainty, and cybersecurity.
  • Development Process: The conceptual, preliminary, and final phases progress from defining system boundaries and functions to decomposing models and interfaces, then integrating validated components.
  • Development Process: Physics-based and data-driven models are independently developed, calibrated, evaluated, and selected according to each process’s requirements rather than technique alone.
  • Development Process: The architecture coordinates update frequencies, data dependencies, communication pathways, execution order, and temporal and physical consistency across components.
  • Operational Framework: Operationally, reactor measurements are processed and assimilated into the digital representation, whose updated state supports estimation, forecasting, anomaly detection, and decision support.
  • Operational Framework: Digital-twin workflows use data, modeling-and-simulation, and visualization layers to transform physical observations into reconstructed or predicted states and user-facing decisions.

4 PUR-1 DT Development Approach

The PUR-1 DT maps nuclear-reactor requirements to real-time acquisition, bidirectional interaction, synchronized modeling, estimation, forecasting, anomaly detection, and predictive control. High-fidelity models and alternative computational approaches address fidelity, explainability, uncertainty, and latency requirements.

  • The PUR-1 DT uses real-time acquisition and bidirectional physical–virtual interaction, while evaluating DT-generated actions through an independent actuation pathway.
  • Dedicated estimation, prediction, AI/ML, PID, and MPC–MHE modules support state estimation, forecasting, anomaly detection, and predictive control within reactor safety-system bounds.
  • High-fidelity neutronic and thermal-hydraulic models reproduce detailed reactor geometry and unobserved physical phenomena, addressing the physical-fidelity requirement.
  • The selected strategy targeted accuracy above 90%, a 10 s forecasting horizon, and monitoring of at least 5 concurrent signals.
  • Model benchmarking, uncertainty quantification, alternative model fidelities, and cybersecurity-capable communications address explainability, confidence, computational cost, and synchronization requirements.

5 PUR-1 DT Configuration

The PUR-1 DT combines two independently controlled physical subsystems with a multilayer virtual asset. It uses live measurements, high-fidelity and surrogate models, diagnostics, estimation, forecasting, and visualization for real-time decision support.

  • 5 PUR-1 DT Configuration: The PUR-1 DT integrates the PUR-1 reactor and CERVEROS testbed with a multilayer virtual asset.Both physical subsystems update the virtual asset, while DT control commands return only to CERVEROS, isolating the PUR-1 control system.
  • 5 PUR-1 DT Configuration: Live reactor and testbed data are combined with high-fidelity physics models, surrogate models, AI/ML diagnostics, and visualization interfaces.This combination represents reactor behavior beyond directly measured quantities.
  • 5 PUR-1 DT Configuration: The configuration supports online state awareness, estimation of unmeasured neutronic and thermal fields, and short-term prediction of reactor response.These capabilities position the DT as an integrated real-time decision-support environment rather than a standalone simulation tool.

6 PUR-1 DT Physical System

The PUR-1 physical system comprises the reactor, the independent CERVEROS testbed, and data-acquisition infrastructure linking them to the virtual asset. CERVEROS introduces measurable moderator-displacement perturbations, while the acquisition architecture supports synchronized operation and bidirectional exchange with the virtual system.

  • 6.1 Purdue University Reactor One (PUR-1): PUR-1 is the first U.S. reactor licensed to operate with a fully digital instrumentation and control system.The facility is mainly used for education and as a gamma and neutron source for research applications.
  • 6.1 Purdue University Reactor One (PUR-1): PUR-1 is a heterogeneous, naturally circulated, light-water-moderated non-power reactor with graphite reflectors, sixteen fuel elements, and three control rods.Its core uses MTR-type HALEU plate fuel in aluminum containers, with graphite assemblies forming the reflector.
  • 6.2 Cyber-Physical Testbed (CERVEROS): CERVEROS is an independently operating cyber-physical testbed installed in the reactor pool, providing additional sensing and a bidirectional actuation interface.Its Auxiliary Moderator Displacement Rod uses a linear actuator and indium foils to introduce external perturbations without interfering with reactor I&C.
  • 6.2 Cyber-Physical Testbed (CERVEROS): AMDR motion perturbs neutron population through moderator displacement, and its effect is characterized by reactivity worth as a function of position.The curve is calculated using the In-hour equation and reactor period derived from measured neutron flux.
  • 6.2 Cyber-Physical Testbed (CERVEROS): The AMDR reactivity-worth dataset was fitted with a two-term sinusoidal basis, and the fitted curve remained within experimental uncertainty bounds.Measurements were collected during incremental AMDR movements while the reactor remained critical and operators compensated for the perturbations.
  • 6.3 Data Acquisition System: The nuclear-grade controller monitors and controls more than 2,000 parameters, while the virtual system must operate at the controller frequency for real-time synchronization.PUR-1 I&C uses a data diode, whereas CERVEROS supports bidirectional exchange through an OPC UA server.

7 PUR-1 DT Virtual System

The PUR-1 DT virtual system combines data processing, physics-based forward and inverse models, AI/ML cybersecurity tools, and visualization to support reactor state analysis and control. High-fidelity models are coupled with surrogate approaches to address real-time computational constraints.

  • The virtual system comprises data, modeling and simulation, and visualization layers.
  • Preprocessing uses filtering, interpolation, and classification to refine noisy, incomplete, or anomalous operational data.
  • Forward Problem Approach: Forward models reconstruct unmeasured neutron-flux, temperature, and coolant-flow distributions from reactor data and physics-based simulations.
  • Forward Problem Approach: The coupled workflow iterates thermal fields, Monte Carlo transport, power profiles, and point kinetics to resolve spatial and transient reactor behavior.
  • Inverse Problem Approach: Inverse models constrain feasible control trajectories by target states and objective functions addressing reactivity effects, fuel depletion, cycle length, and safeguards.
  • Anomaly Detection, Explainability, and Control Modules: The cybersecurity module combines anomaly detection with Random Forest classification and SHAP-based, temporally informed explanations.
  • High-fidelity Monte Carlo and Multiphysics simulations require 2 hours and 8.6 hours respectively on high-performance computing clusters, motivating reduced-order and surrogate models.

8 Cyber-physical Integration

The cyber-physical integration framework coordinates data, models, communications, security, and presentation across the physical and virtual systems. Its synchronization criterion requires relevant end-to-end latency to remain below 1 second.

  • A real-time communication bus coordinates data exchange across DT layers and organizes process inputs and outputs.
  • A unified DeepLynx data warehouse consolidates physical-system and virtual-asset signals while preserving provenance and context.
  • Graph-based exploration represents signals and assets as nodes and relationships as edges to support traceability across DT components.
  • Data adapters refine, validate, and standardize inputs before each process, while surrogate models reduce high-fidelity simulation runtimes.
  • Network Communications: The CERVEROS OPC UA interface exchanges measurements and authorized AMDR actuation commands, with symmetric encryption optionally strengthened by QKD-generated keys.
  • Network Communications: Approximately 390 ms mean latency was measured for up to 2,000 reactor signals across OTP, AES-256, and ASCON configurations.
  • Latency Metrics: Internal latency separates module execution time from presentation time, with three-dimensional field rendering affected by spatial resolution, mesh density, and workstation resources.
  • Latency Metrics: Synchronization is maintained when the relevant end-to-end latency satisfies t_total < 1 s.

9 Benchmarking

The PUR-1 DT’s component models were benchmarked against experimental or operational data, showing generally good agreement across neutronics, thermal-hydraulics, kinetics, and surrogate predictions. The main accuracy limitations occurred at low flux levels and in irradiation-assembly estimates.

  • Monte Carlo Benchmarking: More than 60 gold foils were irradiated at axial and radial core-boundary locations to benchmark the OpenMC neutron-flux model.The campaign measured flux using gold-foil irradiation experiments and detailed modeling of the experimental structure.
  • Monte Carlo Benchmarking: 6.75% average deviation separated experimental and simulated total neutron flux across foil locations.Flux peaked near core-center assemblies and attenuated toward the edges.
  • Monte Carlo Benchmarking: 2.89% average difference was obtained for medium- and high-flux assembly positions, while correlation was lower at low flux levels.The result supports the model’s benchmarking validity but identifies weaker agreement in low-flux regions.
  • Multiphysics Benchmarking: 1.37% average percentage difference was obtained between COMSOL pool-temperature predictions and experimental data.The comparison used 153 mesh points within 20 inches of the pool surface over the experimental time span and power inputs.
  • Point Kinetics Benchmarking: 6.89% average percentage difference was found between point-kinetics predictions and measured neutron population across startup-to-shutdown scenarios.Forecasting was not activated because this benchmark used historical operational data offline.
  • Surrogate-Model Benchmarking: 3.62% average percentage difference was achieved for the predicted full-core neutron-flux field, while irradiation-assembly estimates differed by 17.81% from experimental flux.The surrogate reproduced major spatial characteristics, with largest deviations near control rods, the source assembly, and field boundaries.

10 Use case

The PUR-1 DT was evaluated over repeated power transitions using synchronized physics-based models and surrogate models to estimate reactor state and forecast behavior. Integrated power predictions agreed with measurements while latency analysis exposed visualization and encrypted-communication constraints for neutron-flux presentation.

  • Operational-cycle evaluation: The use case repeated reactor transitions from 0% to 10%, 65%, and back to 0%, combining PKE, Monte Carlo, multiphysics, and surrogate models.Process ordering varied between steady-state and transient operation.
  • State estimation and forecasting: The DT supplied estimates of unmeasured neutron-population behavior and temperature distributions from physical-system observations.Preprocessed data moved through the data layer into modeling and simulation functions.
  • State estimation and forecasting: Control-rod sensitivities shaped keff estimates: SS1 had the highest reactivity worth, SS2 supported power changes, and RR compensated for steady-state drifts.The varying rod sensitivities were reflected in the slopes of the keff relationship.
  • State estimation and forecasting: Approximately 100 seconds of COMSOL computation projected heat-flux and temperature evolution from t_N+100 to t_N+200.Thermohydraulic predictions used the current reactor state as the initial condition and were updated at a lower frequency.
  • Integrated performance: 9.2% average percentage difference separated predicted reactor power from physical-system measurements across the operational cycle.The discrepancy was attributed primarily to possible control-rod-worth miscalibration and propagated errors from individual modules.
  • Latency evaluation: All three workflows stayed below the 1 s no-delay threshold, but neutron-flux presentation periodically exceeded the 610 ms budget after encrypted communication was included.The neutron-flux surrogate itself remained below both thresholds when GUI rendering and presentation latency were excluded.

11 Lessons Learned

Lessons from PUR-1 DT development emphasize system-level latency analysis, computational trade-offs, sensor-data conditioning, and continuing model reassessment. High-fidelity models and surrogate training can impose substantial computational costs, while evolving operating conditions can invalidate offline models.

  • System integration: System-level latency must include sequential dependencies, communication, and visualization rather than evaluating modules independently.This motivated surrogate models for time-critical processes, critical-path analysis, and lower-frequency visualization.
  • Computational efficiency: Uniformly fine meshing was computationally impractical because the reactor pool is approximately 5 m deep while fuel plates are approximately 2 mm thick.Simulation runtimes exceeded 28 h per case, motivating nonuniform meshing.
  • Computational efficiency: Each initial OpenMC simulation required approximately 2 h, making generation of the 2,500-run training dataset substantially time-consuming.A parametric study optimized batches and particles per batch against runtime and experimental agreement.
  • Data quality: Noisy AMDR measurements and ultrasonic reflections produced intermittent position outliers during operation.Mitigations included moving-average filtering and repositioning the ultrasonic sensor and target surface.
  • Model validity: Offline validation is insufficient when physical conditions move beyond training regimes or real-world noise and communication disturbances are underrepresented.Data-driven models therefore require periodic reassessment and, when necessary, recalibration or retraining.

12 Discussion and Conclusions

The PUR-1 cyber-physical digital twin achieved real-time synchronization and accurate physics-based benchmarking while supporting state identification, forecasting, and operator decision support. Its remaining limitations concern transient sensitivity, localized surrogate discrepancies, computational update rates, and cybersecurity requirements.

  • The DT synchronized with the reactor at 1 Hz, while flux-mapping deviations stayed below 10% and thermal-field deviations were approximately 2%.Benchmarking used gold foil activation for neutron flux distributions and pool-temperature measurements for thermal-hydraulic fields.
  • State identification, short-term forecasting, and operator decision support extended observability beyond instrumentation limits and provided predictive insight for reactor operation.
  • 9.2% average percentage difference between DT predictions and physical-system measurements indicated satisfactory predictive consistency throughout the full operational cycle.Simulation-trained surrogate models enabled real-time prediction while retaining physical interpretability.
  • PKE and neutronic surrogate workflows met the 1 s synchronization requirement including encrypted communication overhead, whereas high-resolution flux visualization could be updated asynchronously.
  • Forecasting remains sensitive to control-rod reactivity-worth uncertainty and sensor artifacts during transients, with larger localized flux-surrogate discrepancies in strong spatial gradients.The Multiphysics model also updates less frequently because of its higher computational cost, while continuous data exchange requires robust cybersecurity defenses.
  • The PUR-1 DT provides a reference architecture for potential extensions to autonomous control, predictive maintenance, operator training, and smart-grid integration.
Loading 2608.30186v1…