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Constrained Sensing and Reliable State Estimation with Shallow Recurrent Decoders on a TRIGA Mark II Reactor

This paper presents the first application of Shallow Recurrent Decoder (SHRED) networks to a deployed TRIGA Mark II nuclear reactor, demonstrating their ability to accurately reconstruct full state fields in real-time using both synthetic and experimental temperature data while maintaining robustness against sensor noise and model discrepancies.

Original authors: Stefano Riva, Carolina Introini, Josè Nathan Kutz, Antonio Cammi

Published 2026-09-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Stefano Riva, Carolina Introini, Josè Nathan Kutz, Antonio Cammi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Inside a nuclear reactor, the core is a place of intense heat and invisible forces, where water flows, fuel burns, and energy is released. To keep such a system safe and efficient, engineers need to know exactly what is happening inside at every moment. They need to track the temperature of the water, the speed of its flow, and the pressure building up within the fuel channels. However, the inside of a reactor is a hostile environment; it is too hot and too radioactive for most instruments to survive for long. This leaves scientists with a difficult puzzle: they have only a handful of sensors, placed in a few specific spots, trying to guess the condition of the entire machine. It is like trying to understand the weather of a whole continent by looking at the sky through just two small windows. For decades, solving this puzzle has required complex mathematical models that are slow to run and often struggle when the real world does not match the theory perfectly.

A team of researchers has now tested a new, faster way to solve this problem using a type of artificial intelligence called a shallow recurrent decoder. This method was designed to take the limited, noisy data from a few sensors and reconstruct the full, detailed picture of the reactor's interior in real time. The researchers applied this technique to the TRIGA Mark II, a well-known research reactor at the University of Pavia in Italy. They wanted to see if this new tool could accurately guess the state of the reactor even when the sensors were placed in "quiet" spots where the water barely moved, and whether it could correct itself when the computer model disagreed with the actual measurements from the real reactor.

The team began by creating a detailed computer simulation of the reactor, which served as a perfect reference for how the system should behave. They then trained their artificial intelligence using data from this simulation, but with a twist: they told the system to pretend it only had access to temperature readings from two very specific channels. One channel was located on the outside edge of the reactor core, where the water moves slowly, and the other was hidden behind a control rod, a place where the flow is shielded and difficult to observe. These are the kinds of "bad" locations where sensors are often forced to sit due to physical constraints. Despite starting with such limited and unexciting data, the system learned to predict the temperature, speed, and pressure of the water everywhere else in the reactor. The results were strikingly accurate. The system reconstructed the entire flow field with an average error of less than four percent compared to the perfect simulation. It successfully figured out the behavior of the water in places where it had no sensors at all, proving that it could learn the hidden dynamics of the system from just a few quiet points.

The researchers then took the next step, moving from the perfect world of the computer simulation to the messy reality of the actual reactor. They used temperature data recorded during a real experiment where the reactor was heated from a cold start to full power. In this phase, the computer model they had trained on did not perfectly match the real world; for instance, the model did not account for some cold water circulating from the top of the pool, which caused the real sensors to read lower temperatures than the simulation predicted. When the researchers fed the real experimental data into their trained system, the artificial intelligence noticed the difference. Instead of blindly following the flawed computer model, it adjusted its predictions to align more closely with the real measurements. It effectively "corrected" the background knowledge of the model, reducing the error between the prediction and the actual temperature readings. In some cases, the new method was significantly more accurate than the original computer simulation alone.

This work demonstrates that this new type of neural network is not just a theoretical exercise but a practical tool that can handle the constraints of real engineering. It showed that the system is robust enough to work even when sensors are placed in poor locations and flexible enough to update its understanding when faced with new, real-world data. The researchers found that the system could learn the complex physics of the reactor in just a few minutes on a standard laptop, a speed that would be impossible for traditional, heavy-duty simulation methods. While the current study focused on a specific, normal operating scenario, the results suggest that this approach could eventually help build "digital twins" of nuclear reactors—virtual copies that monitor the real plant in real time, ensuring safety and efficiency even when the physical sensors are sparse or the conditions change. The study confirms that with the right data-driven approach, we can see the invisible heart of a nuclear reactor with clarity and confidence.

Technical Summary: Constrained Sensing and Reliable State Estimation with Shallow Recurrent Decoders on a TRIGA Mark II Reactor

Problem Statement
Reconstructing the internal state of nuclear reactors from sparse and noisy sensor measurements is a critical challenge for monitoring and control. Nuclear reactors are complex, multi-physics systems operating in harsh environments where sensor placement is restricted by physical access, economic constraints, and safety regulations. Consequently, state estimation tasks are ill-posed inverse problems characterized by: (i) limited and non-arbitrary sensor positioning; (ii) the presence of unobservable fields (e.g., velocity, pressure, turbulence) that must be inferred indirectly; and (iii) discrepancies between mathematical models (used for training) and real-world data due to modeling assumptions or parameter uncertainties. Traditional Data Assimilation (DA) methods, such as Kalman Filtering or variational approaches, often require computationally expensive optimization of high-dimensional Partial Differential Equation (PDE) systems, making them unsuitable for quasi-real-time applications.

Methodology: SHRED Architecture
This work applies the Shallow Recurrent Decoder (SHRED) network, a data-driven architecture designed to map temporal trajectories of sparse measurements to a full system state space. The methodology relies on the following components:

Architecture: SHRED combines a Long Short-Term Memory (LSTM) network with a Shallow Decoder Network (SDN). The LSTM captures temporal dynamics from sparse sensor time-series, while the SDN decodes a latent representation into the full state space.
Theoretical Basis: The approach leverages the Takens embedding theorem, substituting dense spatial data at a single instant with a time-trajectory of sensor measurements. It is grounded in the separation of variables for PDEs, decoupling temporal behavior from spatial structures.
Dimensionality Reduction: To handle high-dimensional state vectors (e.g., $10^4$ to $10^6$ degrees of freedom), the method employs Singular Value Decomposition (SVD) or Proper Orthogonal Decomposition (POD). The neural network operates in a compressed latent space (reduced order), mapping sensor measurements to reduced coefficients rather than the full state directly.
Ensemble Strategy: To handle noisy data and improve robustness, the framework trains an ensemble of SHRED models using different subsets of sensor configurations. The final prediction is the mean of these models, accompanied by a confidence interval.
Training Efficiency: By operating in the compressed space, training is computationally efficient (minutes on a standard laptop) and requires minimal hyperparameter tuning.

Application and Experimental Setup
The study focuses on the TRIGA Mark II research reactor (250 kW) at the University of Pavia. The background model is a Computational Fluid Dynamics (CFD) simulation of the reactor core, representing a fluid dynamics model with a state vector comprising temperature ( $T$ ), velocity ( $u$ ), pressure ( $p$ ), turbulent kinetic energy ( $\kappa$ ), and dissipation rate ( $\omega$ ).

Data Sources: The study utilizes both synthetic data from the CFD model and experimental data from a 2016 campaign involving Pt1000 temperature sensors in specific core channels.
Constraints: Sensors are restricted to "low-dynamics" channels (e.g., peripheral channels or those shielded by control rods) to test the architecture's robustness against suboptimal positioning. Only temperature is directly observable; other fields are unobservable.

Key Contributions
The paper claims four primary contributions:

First Deployment Application: This is the first application of SHRED to a deployed nuclear reactor (TRIGA Mark II), moving beyond conceptual designs or small experimental facilities.
Hybrid Data Integration: The work integrates hybrid synthetic and experimental data within the SHRED framework, testing the model's ability to handle real-world discrepancies.
Robustness Assessment: A systematic evaluation of SHRED under physically constrained, low-dynamics sensor locations demonstrates that the architecture is agnostic to sensor positioning.
Self-Correction Evaluation: A quantitative assessment of the architecture's capability to self-correct when model-to-data discrepancies exist, specifically evaluating its ability to update background knowledge using real measurements.

Results

Synthetic Reconstruction: Using synthetic data from constrained sensors (channels with low dynamics), SHRED accurately reconstructed the full state space. The average relative error in the Euclidean norm was below 4% for all fields, including unobservable ones like velocity and turbulence. The ensemble strategy provided reliable confidence intervals.
Experimental Validation and Self-Correction: When tested with experimental data, SHRED demonstrated the ability to correct the background CFD model.
- In scenarios where experimental data deviated from the CFD model (e.g., due to unmodeled recirculation phenomena in the upper pool), SHRED adjusted its predictions to better align with the experimental measurements.
- Quantitative analysis showed a reduction in Root Mean Square Error (RMSE) compared to the baseline CFD. For instance, when trained on Hole 9 data and tested on Hole 3, the mean RMSE dropped from 2.155 K (CFD) to 1.032 K (SHRED).
- The architecture successfully recognized discrepancies between the model and reality, rescaling its output to compensate, though it did not perform a complete physical data assimilation (e.g., updating the governing equations).

Significance and Claims
The paper posits that SHRED offers a robust, interpretable, and computationally efficient solution for nuclear reactor monitoring and control, particularly for building digital twins. Its significance lies in:

Sensor Agnosticism: The method does not require optimal sensor placement, making it suitable for systems with strict physical constraints.
Real-Time Potential: The rapid training and inference capabilities make it viable for real-time state estimation, unlike traditional DA methods burdened by high computational costs.
Handling Uncertainty: The ensemble approach provides confidence intervals, crucial for safety-critical applications.
Model Updating: The ability to partially correct background model discrepancies using real data suggests a pathway for adaptive monitoring systems.

The authors acknowledge limitations, noting that the current implementation operates in reconstruction mode (no forecasting outside the observed window) and that the correction capability is limited to magnitude rescaling rather than a full physical data assimilation process. Future work is proposed to integrate SHRED into a true data assimilation framework and extend its application to parametric and accidental transients.

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