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

TL;DR

SHRED, a shallow decoding strategy based on an LSTM encoder combined with a shallow decoder, reconstructs the full reactor state from sparse measurements in real time. It uses a latent dimension $r=64$ and a lag length $L\approx 30$ in time-delay embeddings, with the high-dimensional state projected via POD/SVD modes. On the TRIGA Mark II CFD model, synthetic data yield average relative errors below $2\%$ for most fields; experimental data show SHRED's ability to update a background model toward observations. These results support SHRED as a viable fast offline tool for reactor monitoring and digital twins, with future work integrating a data assimilation framework and SINDy-SHRED for interpretable dynamics.

Abstract

Shallow Recurrent Decoder networks are a novel data-driven methodology able to provide accurate state estimation in engineering systems, such as nuclear reactors. This deep learning architecture is a robust technique designed to map the temporal trajectories of a few sparse measures to the full state space, including unobservable fields, which is agnostic to sensor positions and able to handle noisy data through an ensemble strategy, leveraging the short training times and without the need for hyperparameter tuning. Following its application to a novel reactor concept, this work investigates the performance of Shallow Recurrent Decoders when applied to a real system. The underlying model is represented by a fluid dynamics model of the TRIGA Mark II research reactor; the architecture will use both synthetic temperature data coming from the numerical model and leveraging experimental temperature data recorded during a previous campaign. The objective of this work is, therefore, two-fold: 1) assessing if the architecture can reconstruct the full state of the system (temperature, velocity, pressure, turbulence quantities) given sparse data located in specific, low-dynamics channels and 2) assessing the correction capabilities of the architecture (that is, given a discrepancy between model and data, assessing if sparse measurements can provide some correction to the architecture output). As will be shown, the accurate reconstruction of every characteristic field, using both synthetic and experimental data, in real-time makes this approach suitable for interpretable monitoring and control purposes in the framework of a reactor digital twin.

Figures (10)

• Figure 1: SHRED architecture applied to the TRIGA MARK II research reactor. Three sensors are used to measure the coolant temperature field. The sensor time series is used to construct a latent temporal sequence model which is mapped to compressive representations of all spatio-temporal field variables. The compressive representations can then be mapped to the original state space by singular value decomposition. The compressive representation allows for laptop level training in minutes even on multiple high-dimensional field variables.
• Figure 2: (a) Photo of the Cherenkov effect at the TRIGA reactor in Pavia, visible after the reactor shutdown following SCRAM; (b) Disposition of the fuel elements (blue with aluminium and light grey with steel cladding) in the current core configuration. Red elements are the control rod, white ones the irradiation channels, dark grey ones the graphite elements, the yellow one the neutron source, and the black dots are the locations of the available coolant temperature measurements.
• Figure 3: Decay of the singular values (left) and relative energy content discarded by the SVD modes (right) for the fields in the state vector $\mathcal{V} = [T, \mathbf{u}, p, \kappa, \omega]$ for the TRIGA Mark II reactor.
• Figure 4: Computational geometry of the TRIGA reactor (shaded in gray): the available positions for sensing are the red and blue channels, being the REG and EXT respectively.
• Figure 5: Comparison of the SHRED reconstruction of the first 5 SVD coefficients of velocity $\mathbf{u}$, temperature $T$ (observed field), pressure $p$, turbulent kinetic energy $\kappa$ and dissipation rate $\omega$, for test time. Dashed curves represent the mean of the SHRED models from ext channels, dotted curves the one from reg channels, the continuous lines are the ground truth (from the full-order data) and the shaded areas highlight the uncertainty regions for the SHRED models.