Author: Stefano Riva
Date: 2025-10-28
Supervisor: Prof. Antonio Cammi (Politecnico di Milano)
Co-Supervisors: Dr. Carolina Introini (Politecnico di Milano), Prof. Nathan Kutz (University of Washington)
The quick and reliable state estimation of what is happening inside a nuclear reactor to retrieve the best possible insight into the status of the system is a significant safety concern within the industry, especially for the new generation of reactors featuring liquid metals as coolant or molten salts as fuel. In these novel designs, the environment is harsher and more hostile than in standard water-cooler reactors, making in-core sensing and monitoring challenging. Therefore, it becomes necessary to investigate the possibility of inferring the state in the whole domain (including inaccessible regions) from few and sparse local observations. To this aim, their information must be coupled with the knowledge provided by background models, usually described by parametric Partial Differential Equations, to seek the optimal state estimation to minimize the distance between models and local measures: this is the general formulation of state estimation within a Data Assimilation framework.
Due to the intrinsically heavy computational costs associated with the numerical solution of mathematical models for engineering systems, this framework requires a low-dimensional representation to ensure a quick, efficient and reliable solution whilst keeping the accuracy at a desired level. This aim can be achieved by exploiting Reduced Order Modelling (ROM) approaches: generally speaking, they aim at finding an optimal (and small) set of spatially-dependent basis functions upon which a surrogate model is generated, allowing for a strong dimensionality reduction and, hence, much lower computational costs, whilst keeping good accuracy. In the past few years, several 'classical' data-driven ROM methods have been proposed to combine local observations with background information of mathematical models, such as the Generalised Empirical Interpolation Method or the Parametrised-Background Data-Weak formulation, which also allows for correcting the background model introducing additional terms for the non-modelled physics. Moreover, the recent developments in Artificial Intelligence have paved the way for new approaches able to merge measures and models: hence, by following the current trend of the industry, in this work, the newly proposed Shallow Recurrent Decoder framework is investigated, an architecture that features low training costs, the ability to deal with nonlinear dynamics and parametric datasets and minimal hyperparameter tuning.
These methods have been tested on benchmark case studies for neutronics and fluid dynamics, the Molten Salt Fast Reactor concept, the TRIGA Mark II reactor, and a real experimental facility (DYNASTY, built at Politecnico di Milano) involving multi-physics models and real measurements: very promising results have been obtained, providing an in-depth investigation of the advantages and disadvantages of these techniques for the state estimation problem in nuclear reactors; this allows for their implementation in digital twins for a safer and more efficient management of engineering systems.
This PhD Thesis aims at pushing the boundaries of open-source software for the nuclear community; hence, I'm happy to share some of the code I used to generate the results in my PhD thesis. The code is organized in Jupyter notebooks. The notebooks are organized into folders, each corresponding to a chapter of the thesis using a git submodule.
- pyforce: https://github.com/ERMETE-Lab/ROSE-pyforce - version 0.1.3 used
- NuSHRED: https://github.com/ERMETE-Lab/NuSHRED
- pDMD: https://github.com/ERMETE-Lab/pDMD
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The thesis LaTeX source is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). You are free to share and adapt the material with appropriate attribution.
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The support-code (in the submodule) are licensed under the MIT License. You are free to use, modify, and distribute the code with attribution.