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38 changes: 20 additions & 18 deletions joss-paper/paper.bib
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Expand Up @@ -5,7 +5,7 @@ @article{DDMOR_CFR
pages = {113105},
year = {2024},
issn = {0029-5493},
doi = {https://doi.org/10.1016/j.nucengdes.2024.113105},
doi = {10.1016/j.nucengdes.2024.113105},
url = {https://www.sciencedirect.com/science/article/pii/S002954932400205X},
author = {Antonio Cammi and Stefano Riva and Carolina Introini and Lorenzo Loi and Enrico Padovani},
keywords = {Hybrid Data-Assimilation, Generalized Empirical Interpolation Method, Indirect Reconstruction, Sensors positioning, Molten Salt Fast Reactor, Noisy data},
Expand Down Expand Up @@ -34,7 +34,8 @@ @misc{RMP_2024
year={2024},
eprint={2401.07300},
archivePrefix={arXiv},
primaryClass={math.NA}
primaryClass={math.NA},
doi = {10.48550/arXiv.2401.07300}
}

@misc{BarattaEtal2023,
Expand All @@ -45,23 +46,24 @@ @misc{BarattaEtal2023
howpublished = {preprint}
}

@book{quarteroni2015reduced,
author = {Quarteroni, A and Manzoni, A and Negri, F},
isbn = {9783319154312},
publisher = {Springer International Publishing},
series = {UNITEXT},
title = {{Reduced Basis Methods for Partial Differential Equations: An Introduction}},
year = {2015},
url = {https://link.springer.com/book/10.1007/978-3-319-15431-2}
@book{rozza_model_2020,
title = {Model {Order} {Reduction}: {Volume} 2: {Snapshot}-{Based} {Methods} and {Algorithms}},
isbn = {978-3-11-067149-0},
url = {https://doi.org/10.1515/9783110671490},
publisher = {De Gruyter},
author = {Rozza, Gianluigi and Hess, Martin and Stabile, Giovanni and Tezzele, Marco and et al.},
year = {2020},
doi = {10.1515/9783110671490},
}

@inproceedings{demo_complete_2019,
title = {A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems},
booktitle = {{MARINE} 2019: {VIII} {International} {Conference} on {Computational} {Methods} in {Marine} {Engineering}},
author = {Demo, Nicola and Tezzele, Marco and Mola, Andrea and Rozza, Gianluigi},
month = may,
pages = {1-12},
year = {2019},
@misc{demo2019complete,
title={A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems},
author={Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza},
year={2019},
eprint={1905.05982},
archivePrefix={arXiv},
primaryClass={math.NA},
doi = {10.48550/arXiv.1905.05982}
}

@article{maday_generalized_2015,
Expand All @@ -84,7 +86,7 @@ @article{introini_stabilization_2023
copyright = {All rights reserved},
issn = {0045-7825},
url = {https://www.sciencedirect.com/science/article/pii/S0045782522007290},
doi = {https://doi.org/10.1016/j.cma.2022.115773},
doi = {10.1016/j.cma.2022.115773},
abstract = {The Empirical Interpolation Method (EIM), and its generalized version (GEIM), are non-intrusive, reduced-basis model order reduction methods hereby adopted and modified to address the problem of optimal placement of sensors and real-time estimation in thermo-hydraulics systems. These techniques have been used to extract the characteristic spatial modes of the system and select a set of points (or functionals) corresponding to the optimal locations for the sensors. Collecting experimental measurements in the available points allows the construction of an empirical interpolation of the fields employed to estimate the variable of interest. However, when these data are affected by noise, the (G)EIM loses its good convergence properties. In this context, stabilization techniques allow good field reconstruction even with noisy data. This work provides an alternative and effective solution to the problem of reconstructing the system state in the presence of experimental data affected by random noise by using the Tikhonov regularization technique. The developed methods have been tested on a simple thermo-fluid dynamics problem known as “two-sided lid-driven differentially heated square cavity”.},
journal = {Computer Methods in Applied Mechanics and Engineering},
author = {Introini, Carolina and Cavalleri, Simone and Lorenzi, Stefano and Riva, Stefano and Cammi, Antonio},
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11 changes: 5 additions & 6 deletions joss-paper/paper.md
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Expand Up @@ -20,18 +20,17 @@ authors:
corresponding: true # (This is how to denote the corresponding author)
affiliation: 1
affiliations:
- name: Energy Department - Nuclear Engineering Division, Nuclear Reactors Group - ERMETE Lab, Politecnico di Milano
- name: Energy Department - Nuclear Engineering Division, Nuclear Reactors Group - ERMETE Lab, Politecnico di Milano, Milan, Italy
index: 1
date: 21 May 2024
bibliography: paper.bib

# # Optional fields if submitting to a AAS journal too, see this blog post:
# # https://blog.joss.theoj.org/2018/12/a-new-collaboration-with-aas-publishing
# aas-doi: 10.3847/xxxxx <- update this with the DOI from AAS once you know it.
# aas-journal: Astrophysical Journal <- The name of the AAS journal.
---

# Summary
Innovative reactor technologies in the framework of Generation IV are usually characterised by harsher and more hostile environments compared to standard nuclear systems, for instance, due to the liquid nature of the fuel or the adoption of liquid salt and molten as coolant. This framework poses more challenges in the monitoring of the system itself; since placing sensors inside the reactor itself is a nearly impossible task, it is crucial to study innovative methods able to combine together different sources of information, namely mathematical models and real data (i.e., measurements) in a quick, reliable and efficient way. These methods fall into the Data-Driven Reduced Order Modelling framework, they can be very useful to learn the missing physics or the dynamics of the problem, in particular, they can be adapted to generate surrogate models able to map the out-core measurements of a simple field (e.g., neutron flux and temperature) to the dynamics of un-observable complex fields (precursors concentration and velocity).

# Statement of need
*pyforce* is a Python library (Python Framework for data-driven model Order Reduction of multi-physiCs problEms) implementing Data-Driven Reduced Order Modelling (DDROM) techniques [@RMP_2024] for applications to multi-physics problems, mainly for the Nuclear Engineering world. These techniques have been implemented upon the dolfinx package [@BarattaEtal2023] (currently v0.6.0), part of the FEniCSx project, to handle mesh generation, integral calculation and functions storage. The package is part of the ROSE (Reduced Order modelling with data-driven techniques for multi-phySics problEms) framework, which investigates mathematical algorithms aimed at reducing the complexity of multi-physics models with a focus on nuclear reactor applications, at searching for optimal sensor positions and at integrating experimental data to improve the knowledge on the physical systems.

![General scheme of DDROM methods [@RMP_2024].\label{fig:darom}](../images/tie_frighter.pdf){ width=80% }
Expand All @@ -40,7 +39,7 @@ The techniques implemented here follow the same underlying idea expressed in Fig

Up to now, the following techniques have been implemented [@DDMOR_CFR;@RMP_2024]:

1. Proper Orthogonal Decomposition (POD) [@quarteroni2015reduced] with Projection and Interpolation [@demo_complete_2019] for the Online Phase
1. Proper Orthogonal Decomposition (POD) [@rozza_model_2020] with Projection and Interpolation [@demo_complete_2019] for the Online Phase
2. Generalised Empirical Interpolation Method (GEIM) [@maday_generalized_2015], either regularised with Tikhonov [@introini_stabilization_2023] or not
3. Parameterised-Background Data-Weak (PBDW) [@maday_parameterized-background_2014]
4. an Indirect Reconstruction [@introini_non-intrusive_2023] algorithm to reconstruct non-observable fields
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