Application of parametric Shallow Recurrent Decoder Network to magnetohydrodynamic flows in liquid metal blankets of fusion reactors

Abstract

Magnetohydrodynamic (MHD) phenomena play a pivotal role in the design and operation of nuclear fusion systems, where electrically conducting fluids (such as liquid metals or molten salts employed in reactor blankets) interact with magnetic fields of varying intensity and orientation, influencing the resulting flow dynamics. The numerical solution of MHD models entails the resolution of highly nonlinear, multiphysics systems of equations, which can become computationally demanding, particularly in multi-query, parametric, or real-time contexts. This study investigates a fully data-driven framework for MHD state reconstruction that integrates dimensionality reduction through Singular Value Decomposition (SVD) with the SHallow REcurrent Decoder (SHRED), a neural network architecture designed to reconstruct the full spatio-temporal state from sparse time-series measurements of selected observables, including previously unseen parametric configurations. The SHRED methodology is applied to a three-dimensional geometry representative of a portion of a WCLL blanket cell, in which lead-lithium flows around a water-cooled tube. Multiple magnetic field configurations are examined, including constant toroidal fields, combined toroidal-poloidal fields, and time-dependent magnetic fields. Across all considered scenarios, SHRED achieves high reconstruction accuracy, robustness, and generalization to magnetic field intensities, orientations, and temporal evolutions not seen during training. Notably, in the presence of time-varying magnetic fields, the model accurately infers the temporal evolution of the magnetic field itself using temperature measurements alone. Overall, the findings identify SHRED as a computationally efficient, data-driven, and flexible approach for MHD state reconstruction, with significant potential for real-time monitoring, diagnostics and control in fusion reactor systems.

Figures (16)

• Figure 1: Schematic representation of the SHRED architecture applied to the considered three-dimensional test case. After compressing the original dataset via SVD, three sensors record the local temporal evolution of the temperature field. The resulting time-series signals are encoded into a latent space through a Long Short-Term Memory (LSTM) network. Subsequently, a Shallow Decoder Network (SDN) maps the latent representation onto a compressed approximation of the full set of spatio-temporal field variables. Finally, the SVD basis is used to reconstruct the corresponding full-order state back-projcting its compressed representation.
• Figure 2: Visual sketch of the selected model geometry. The image of the elementary cell on the left is taken from arena2021demo.
• Figure 3: Overview of the selected magnetic field configurations considered in this analysis: a) constant toroidal magnetic field, b) constant toroidal toroidal + poloidal magnetic field, c) time-varying magnetic field.
• Figure 4: Subdivision of the dataset in training, validation and test snapshots.
• Figure 5: Results for the temperature (first column), velocity (second column) and pressure (third column) for the case with $B_x=0.75 \, T$ at time $t=2\, s$. The first row displays the reference full-order solution while the second row shows the reconstruction produced by the SHRED model. The third row reports the absolute difference between the FOM and the SHRED.