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Magnetohydrodynamic (MHD) effects play a key role in the design and operation of nuclear fusion systems, where electrically conducting fluids (such as liquid metals or molten salts in reactor blankets) interact with magnetic fields of varying intensity and orientation, which affect the resulting flow. The numerical resolution of MHD models involves highly nonlinear multiphysics systems of equations and can become computationally expensive, particularly in multi-query, parametric, or real-time contexts. This work investigates a fully data-driven framework for MHD state reconstruction that combines dimensionality reduction via Singular Value Decomposition (SVD) with the SHallow REcurrent Decoder (SHRED), a neural network architecture designed to recover the full spatio-temporal state from sparse time-series measurements of a limited number of observables. The methodology is applied to a parametric MHD test case involving compressible lead-lithium flow in a stepped channel subjected to thermal gradients and magnetic fields spanning a broad range of intensities. To improve efficiency, the full-order dataset is first compressed using SVD, yielding a reduced representation used as reference truth for training. Only temperature measurements from three sensors are provided as input, while the network reconstructs the full fields of velocity, pressure, and temperature. To assess robustness with respect to sensor placement, thirty randomly generated sensor configurations are tested in ensemble mode. Results show that SHRED accurately reconstructs the full MHD state even for magnetic field intensities not included in the training set. These findings demonstrate the potential of SHRED as a computationally efficient surrogate modeling strategy for fusion-relevant multiphysics problems, enabling low-cost state estimation with possible applications in real-time monitoring and control.