physics.comp-phAug 28, 2026

Real-Time Monitoring of MHD Liquid Metal Flows with Shallow Recurrent Decoders

Authors: Claudio Scardino, Stefano Riva, Carolina Introini, Matteo Lo Verso, Eric Cervi, Antonio Cammi, Laura Savoldi

Organizations: Energy Department, CeSNEF - Nuclear Engineering Division, Politecnico di Milano, Milano · Autodesk Research, 6 Agar Street, London, WC2R 0QE, UK · Argonne National Laboratory, Lemont, IL, 60439, United States of America · MAHTEP Group, Dipartimento Energia “Galileo Ferraris”, Politecnico di Torino, Torino

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Abstract

State estimation in magnetohydrodynamic flows is critical for real-time monitoring of liquid metal blankets in tokamak fusion reactors. Due to the multiphysics nature of these phenomena, high-fidelity simulations are computationally prohibitive for real-time applications. This work investigates a data- driven Reduced Order Model framework: the Shallow Recurrent Decoder (SHRED) coupled with Principal Component Analysis, to map sparse temperature measurements to the full thermo-hydraulic system's state. The major contribution of this work lies in the two-parameter analysis of a fully three-dimensional domain representative of the DEMO breeding blanket configuration. Here, the flow is subjected to an external magnetic field varying in direction and intensity and is hindered by two cylinders acting as a water-cooling system, which impose a temperature boundary condition on their surfaces. This double-parametric magnetic variation induces nonlinear transitions in the flow dynamics, ranging from chaotic behavior at low magnetic field intensities to laminarized regimes at high intensities, characterized by the formation of asymmetric side layers at an inclination angle of 30 degrees. SHRED reconstruction maintains a mean relative error of approximately 5% for the temperature, pressure, and velocity fields. This accuracy is maintained across both weak and strong magnetic fields, ranging from 0.075 T to 0.300 T, and for inclination angles from 5 to 30 degrees, reflecting its dominant toroidal component. These errors are only slightly larger than the lower error bound dictated by low-rank truncation. The results establish SHRED as a reliable state estimator for complex and realistic engineering applications involving completely unseen parametric scenarios and validate it as an accurate real-time state estimation technique suitable for online monitoring and control of real facilities.

Figures & tables

Figure 1: SHallow REcurrent Decoder architecture & Reduced Order Modeling.
Figure 2: Simplified elementary cell of a breeding blanket: geometry and mesh, together with the representation of the applied external magnetic field.
Figure 3: Train, test and validation splitting. Training angles, increasing NtrN_{\text{tr}} , are added to the previous set of training angles, with the exception of the first two training set with only one and two angles.
Figure 4: Principal component analysis on training data set for Ntr=11N_{tr}=11 .
Figure 5: On top, the mean relative errors for the velocity, pressure, and temperature fields are shown as a function of the number of training angles, both for sensor positions randomly chosen, according to the agnosticism of SHRED, and for the optimal sensor placement determined by the DEIM algorithm. Below, the saturation behavior of the mremre as the number of angles increases is represented, expressing the data efficiency of SHRED and its generalization capability.
Figure 6: Comparison of the normalized velocity field between DEIM-SHRED with 11 training angles and standard SHRED with only one training angle αtrain=\alpha_{train}= 17.5°.
Figure 7: Comparison of the normalized temperature field between DEIM-SHRED with 11 training angles and standard SHRED with only one training angle αtrain=\alpha_{train}= 17.5°.
Figure 8: Train, test and validation splitting for the magnetic field intensity. Increasing NtrN_{\text{tr}} , new training cases are added to the previous set of training magnetic fields.
Figure 9: Principal component analysis on training data set for Ntr=15N_{tr}=15 .
Figure 10: Temporal evolution of the first three PCA coefficients, as predicted by the SHRED, for the different fields and different values of magnetic field test. As expected for the pressure field, the first two PCA coefficients are completely flat, highlighting the absence of temporal dynamics, with the exception of low-importance dynamics appearing in subsequent modes, according to the hierarchy of the PCA modes.
Figure 11: SHRED normalized reconstruction of the velocity field for Bext=0.3B_{\text{ext}}=0.3 T at t=2.5t=2.5 s, together with the absolute error and ensemble uncertainty.
Figure 12: Mean relative errors for each field and for each value of the test magnetic field intensity, as a function of the relative training set size.
Figure 13: Test, train and validation splitting for a double parametric case.
Figure 14: Principal component analysis on training data set for Ntr=40N_{tr}=40 .
Figure 15: Mean relative error as a function of the inclination angle and as a function of the magnetic field intensity together with the SVD limit.
Figure 16: SHRED normalized reconstruction of the velocity field for ∣B∣=0.3|B|=0.3 T α=30\alpha=30 ° at t=2.5t=2.5 s, together with the absolute error and ensemble uncertainty. The neural network effectively captures the formation of a single side layer on the top, accordingly to the specific inclination angle.
Figure 17: SHRED normalized reconstruction of the temperature field for ∣B∣=0.3|B|=0.3 T α=30\alpha=30 ° at t=2.5t=2.5 s, together with the absolute error and ensemble uncertainty.
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