Shallow Recurrent Decoder for Nuclear Reactors Applications (NuSHRED)

This repository collects the codes regarding the application of the Shallow REcurrent Decoder (SHRED) method to Nuclear Reactors systems 🏭⚛️

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📄 Related Publications

This repository serves as complementary code to the following papers:

• [P1] Riva, S., Introini, C., Cammi, A., & Kutz, J. N. (2025). Robust State Estimation from Partial Out-Core Measurements with Shallow Recurrent Decoder for Nuclear Reactors. Progress in Nuclear Energy, vol. 189, pp. 105928

• [P2] Riva, S., Introini, C., Kutz, J. N. & Cammi, A. (2025). Towards Efficient Parametric State Estimation in Circulating Fuel Reactors with Shallow Recurrent Decoder Networks

• [P3] Riva, S., Missaglia A., Introini, C., Kutz, J. N. & Cammi, A.(2026). From Models To Experiments: Shallow Recurrent Decoder Networks on the DYNASTY Experimental Facility

• [P4] Riva, S., Introini, C., Cammi, A., & Kutz, J. N. (2025). Constrained Sensing and Reliable State Estimation with Shallow Recurrent Decoders on a TRIGA Mark II Reactor.

• [P5] Riva, S., Introini, C., Kutz, J. N. & Cammi, A., (2026). Multi-Fidelity Learning with Shallow Recurrent Decoders for Reactor Physics Applications.

Upcoming works: two preprints on arxiv have been submitted on the application of SHRED to Fusion MHD systems (code will be released soon).

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📊 Simulation Data

The compressed simulation datasets are available on Zenodo:

• [D1] Molten Salt Fast Reactor (MSFR) in the accidental scenario Unprotected Loss Of Fuel Flow (ULOFF) - Single Transient (Reconstruction mode)
• [D2] Molten Salt Fast Reactor (MSFR) in the accidental scenario Unprotected Loss Of Fuel Flow (ULOFF) - Parametric Transients
• [D3] DYNASTY Experimental Facility - Single Transient (Reconstruction & Prediction mode) and Parametric Transients
• [D4] CFD model of TRIGA Mark II Reactor - Single Transient (Reconstruction mode)
• [D5] Neutronics Model using Diffusion and Point Kinetics LRA benchmark reactor

🎥 If you want to know more about the SHRED method for nuclear reactors, check out this YouTube video!

You can use the script Code/download_datasets.py to download the datasets (if files argument is not specified, all datasets will be downloaded):

python Code/download_datasets.py --files D1 D2

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🏗️ Foundations of SHRED

The SHRED method was first proposed and developed in this paper:

• J. Williams, O. Zahn and J. N. Kutz, Sensing with shallow recurrent decoder networks, Proc. R. Soc. A, 2024

📌 The original code base is available here: github.com/Jan-Williams/pyshred.

This repository also builds upon a related implementation:

• Matteo Tomasetto, Jan P. Williams, Francesco Braghin, Andrea Manzoni, J. Nathan Kutz, Reduced Order Modeling with Shallow Recurrent Decoder Networks, Nature Communications, 2025

📌 Improvements for parametric datasets are available here (collaborative between Matteo Tomasetto and Stefano Riva): github.com/MatteoTomasetto/SHRED-ROM

Additionally, the pyforce package is used for sensor placements and EIM/GEIM comparison in P1. See:

• Riva et al. (2024)
• Cammi et al. (2024)

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📂 Repository Structure

📁 shred/ → Modules for the implementation of the SHRED network from github.com/Jan-Williams/pyshred and github.com/MatteoTomasetto/SHRED-ROM

📁 Code/ → Subfolders corresponding to the applications of SHRED in nuclear reactor concepts, with datasets associated as follows:

	MSFR-ULOFF D1	MSFR-ULOFF D2	DYNASTY D3	TRIGA D4	LRA D5
P1	✅
P2		✅
P3			✅
P4				✅
P5					✅

▶️ How to Execute

1️⃣ Clone or download the repository.

2️⃣ Download the datasets and move them into the appropriate directory.

3️⃣ Install the required dependencies:

Base install:

pip install -r requirements.txt

P1 additionally requires an older version of pyforce (not compatible with v1.0.0), available at github.com/ERMETE-Lab/ROSE-pyforce for some notebooks. For assistance running P1, please contact stefano.riva@polimi.it directly.

P5 additionally requires FEniCSx (dolfinx v0.10.0) and its dependencies (gmsh, mpi4py, petsc4py, ufl, basix, pyvista) if you want to generate the data yourself. Install via conda:

conda install -c conda-forge fenics-dolfinx=0.10.0 gmsh mpi4py pyvista

See the P5 README for further details.

Note: All the SHRED-related code require the base pip install -r requirements.txt only.

Two simple tutorials are available in the Tutorial/ folder for Kolmogorov 2D Flow for single and multiparametric datasets, which can be executed as Jupyter notebooks.

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📬 Contact Information

For inquiries, please contact: 📧 stefano.riva@polimi.it, carolina.introini@polimi.it, antonio.cammi@polimi.it, kutz@uw.edu.

For issues or bugs, refer to the GitHub Issues section of this repository.

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📊 Results

📌 Paper 1

Fast Flux $\phi_1$	Temperature $T$	Velocity $\mathbf{u}$

📌 Paper 2

Out-Core Sensing (Fast Flux)

Fast Flux $\phi_1$	Temperature $T$	Velocity $\mathbf{u}$	Precursors Group 1 $c_1$

Mobile Sensors (First Group of Precursors)

Fast Flux $\phi_1$	Temperature $T$	Velocity $\mathbf{u}$	Precursors Group 1 $c_1$

Mobile Probes (only position measaured)

Fast Flux $\phi_1$	Temperature $T$	Velocity $\mathbf{u}$	Precursors Group 1 $c_1$

📌 Paper 3

Case	Visualization
Parametric Verification
Parametric Validation
Prediction Validation

📌 Paper 4

Temperature $T$	Velocity $\mathbf{u}$

📌 Paper 5