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

arXiv: https://arxiv.org/abs/2510.12368 · HTML: https://mlsanity.com/paper/2510.12368/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 81 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs](https://mlsanity.com/paper/2001.04001/) (2020)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning](https://mlsanity.com/paper/2101.00554/) (2021)
- [Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition](https://mlsanity.com/paper/1409.5496/) (2014)
- [Reduced Order Modeling with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2502.10930/) (2025)
- [Deep Neural Operator Driven Real Time Inference for Nuclear Systems to Enable Digital Twin Solutions](https://mlsanity.com/paper/2308.07523/) (2023)
- [Leveraging arbitrary mobile sensor trajectories with shallow recurrent decoder networks for full-state reconstruction](https://mlsanity.com/paper/2307.11793/) (2023)
- [Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach](https://mlsanity.com/paper/2501.08339/) (2025)
- [Deep Operator Learning for High-Fidelity Fluid Flow Field Reconstruction from Sparse Sensor Measurements](https://mlsanity.com/paper/2412.08009/) (2024)
- [Constrained optimization of sensor placement for nuclear digital twins](https://mlsanity.com/paper/2306.13637/) (2023)
- [From Models To Experiments: Shallow Recurrent Decoder Networks on the DYNASTY Experimental Facility](https://mlsanity.com/paper/2503.08907/) (2025)
- [TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functions](https://mlsanity.com/paper/2409.00244/) (2024)
- [Towards Efficient Parametric State Estimation in Circulating Fuel Reactors with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2503.08904/) (2025)

## Built on by (most cited first, 3 of 3)

- [Application of parametric Shallow Recurrent Decoder Network to magnetohydrodynamic flows in liquid metal blankets of fusion reactors](https://mlsanity.com/paper/2604.02139/) (2026)
- [Surrogate models for nuclear fusion with parametric Shallow Recurrent Decoder Networks: applications to magnetohydrodynamics](https://mlsanity.com/paper/2603.10678/) (2026)
- [Real-Time Monitoring of MHD Liquid Metal Flows with Shallow Recurrent Decoders](https://mlsanity.com/paper/2608.28366/) (2026)

## Abstract (arXiv)

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. The architecture was successfully applied to the Molten Salt Fast Reactor concept; now, this work considers the performance of Shallow Recurrent Decoders on a deployed reactor concept. 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 objectives of this work are therefore: 1) presenting the first application of SHRED to a deployed nuclear reactor (TRIGA Mark II); 2) the integration of hybrid synthetic/experimental data within the SHRED framework; 3) a systematic assessment of SHRED robustness under physically constrained, low-dynamics sensor locations; and 4) a quantitative evaluation of SHRED self-correction capability when model-to-data discrepancies are present. Indeed, this approach is capable of accurately reconstruct every field of interest in real-time, using both synthetic (with an average relative error lower than 4% in euclidean norm) and experimental data (with a RMSE of 1.52 K on the temperature, compared of 1.85 K of the CFD), making it suitable for interpretable monitoring and control purposes in the context of building digital twins for nuclear reactors.