The development of Digital Twins for next-generation nuclear reactors requires robust methodologies capable of reconstructing high-dimensional, multi-physics fields from sparse, partial, and noisy sensor data. The state estimation problem in nuclear reactors is characterized by different challenges: (i) reactors are complex systems with multi-physics and multi-scale phenomena; (ii) the environment is hostile due to high temperature or neutron fluence, which generally make in-core sensing a challenging task; (iii) not all quantities of interest are accessible: for example, it is easy to measure temperature or neutron flux, but nearly impossible to observe velocity. This work addresses these challenges using Shallow Recurrent Decoder (SHRED) networks \cite{RIVA2025105928, shredrom}. SHRED is a scientific Machine Learning paradigm that reconstructs the spatio-temporal data from sparse sensors: the architecture, composed of a recurrent unit and a shallow decoder, is agnostic to sensor placement and offers significant advantages regarding data requirements and computational efficiency. Additionally, the combination of SHRED with Singular Value Decomposition facilitates compressive, laptop-level training. The capabilities of SHRED are demonstrated across three distinct cases, validating the method against both numerical and experimental data: (i) Molten Salt Fast Reactor \cite{RIVA2025105928}, where SHRED successfully infers neutronic and thermal-hydraulic fields during different accidental scenarios using only out-of-core measurements of a single field; (ii) the TRIGA Mark II Reactor \cite{riva2025constrainedsensingreliablestate}, focused on the reconstruction of real 3D fluid dynamics model, including the use of real experimental data; (iii) the DYNASTY Facility \cite{introini2025modelsexperimentsshallowrecurrent}, where the architecture bridges the gap between models and experiments by fusing simulation data with real temperature measurements, acting as validation of the approach on a real system. This work addresses critical challenges of monitoring coupled physics in harsh environments with limited instrumentation: by providing accurate, real-time state reconstruction, SHRED establishes itself as a foundational technology for monitoring nuclear reactors.