Merge pull request #5 from Steriva/main

Add joss-paper and related Github Action

.github/workflows/draft-pdf.yml

@@ -0,0 +1,30 @@
+name: Draft PDF
+on:
+  workflow_dispatch:
+  push:
+    paths:
+      - joss-paper/paper.md
+      - joss-paper/paper.bib
+      - .github/workflows/draft-pdf.yml
+
+jobs:
+  paper:
+    runs-on: ubuntu-latest
+    name: Paper Draft
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+      - name: Build draft PDF
+        uses: openjournals/openjournals-draft-action@master
+        with:
+          journal: joss
+          # This should be the path to the paper within your repo.
+          paper-path: joss-paper/paper.md
+      - name: Upload
+        uses: actions/upload-artifact@v4
+        with:
+          name: paper
+          # This is the output path where Pandoc will write the compiled
+          # PDF. Note, this should be the same directory as the input
+          # paper.md
+          path: joss-paper/paper.pdf

.gitignore

@@ -72,6 +72,9 @@ instance/
 # Scrapy stuff:
 .scrapy
 
+# Joss-Paper Compiler
+joss-paper/joss-compiler/
+
 # Sphinx documentation
 docs/_build/
 

joss-paper/paper.bib

@@ -0,0 +1,117 @@
+@article{DDMOR_CFR,
+title = {Data-driven model order reduction for sensor positioning and indirect reconstruction with noisy data: Application to a Circulating Fuel Reactor},
+journal = {Nuclear Engineering and Design},
+volume = {421},
+pages = {113105},
+year = {2024},
+issn = {0029-5493},
+doi = {https://doi.org/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},
+abstract = {Sensor positioning and real-time estimation of non-observable fields is an open question in the nuclear sector, especially for advanced nuclear reactors. In Circulating Fuel Reactors (CFR), liquid fuel and coolant are homogeneously mixed, and thus these reactors will not have internal structures, making sensor positioning in the primary circuit, including the core, an unresolved problem, making most of the core blind to sensors. Thus, the possibility of estimating the system state in the whole domain using a few local measurements has important implications for safety, monitoring, and control both in nominal and accidental conditions. In this context, the integrated Model Order Reduction and Data Assimilation framework offers intriguing opportunities to reliably combine experimental data and background knowledge from a reduced mathematical model. This work discusses and applies innovative methods within this framework, based on the Generalized Empirical Interpolation and the Indirect Reconstruction algorithms, to a proposed concept of CFR. This work aims to identify the optimal sensor positioning within the core and assess the feasibility of reconstructing the quantities of interest starting only from transient sparse data on fuel temperature, possibly noisy, and testing the predictive capabilities of the discussed methods.}
+}
+
+
+@article{weller_tensorial_1998,
+	title = {A {Tensorial} {Approach} to {Computational} {Continuum} {Mechanics} using {Object}-{Oriented} {Techniques}},
+	volume = {12},
+	url = {http://dx.doi.org/10.1063/1.168744},
+	doi = {10.1063/1.168744},
+	number = {6},
+	journal = {Computers in Physics},
+	author = {Weller, H G and Tabor, G and Jasak, H and Fureby, C},
+	year = {1998},
+	note = {Publisher: AIP},
+	keywords = {c, openfoam 76m12-finite-volume-methods-in-fluid-mec},
+	pages = {620--631},
+}
+
+
+@misc{RMP_2024,
+      title={Multi-Physics Model Bias Correction with Data-Driven Reduced Order Modelling Techniques: Application to Nuclear Case Studies}, 
+      author={Stefano Riva and Carolina Introini and Antonio Cammi},
+      year={2024},
+      eprint={2401.07300},
+      archivePrefix={arXiv},
+      primaryClass={math.NA}
+}
+
+@misc{BarattaEtal2023,
+  title     = {{DOLFINx}: the next generation {FEniCS} problem solving environment},
+  author    = {Baratta, Igor A. and Dean, Joseph P. and Dokken, J{\o}rgen S. and Habera, Michal and Hale, Jack S. and Richardson, Chris N. and Rognes, Marie E. and Scroggs, Matthew W. and Sime, Nathan and Wells, Garth N.},
+  doi       = {10.5281/zenodo.10447666},
+  year      = {2023},
+  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}
+}
+
+@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},
+}
+
+@article{maday_generalized_2015,
+	title = {The {Generalized} {Empirical} {Interpolation} {Method}: {Stability} theory on {Hilbert} spaces with an application to the {Stokes} equation},
+	volume = {287},
+	url = {http://dx.doi.org/10.1016/j.cma.2015.01.018},
+	doi = {10.1016/j.cma.2015.01.018},
+	abstract = {The Generalized Empirical Interpolation Method (GEIM) is an extension first presented by Maday and Mula in Maday and Mula (2013) in 2013 of the classical empirical interpolation method (presented in 2004 by Barrault, Maday, Nguyen and Patera in Barrault etal. (2004)) where the evaluation at interpolating points is replaced by the more practical evaluation at interpolating continuous linear functionals on a class of Banach spaces. As outlined in Maday and Mula (2013), this allows to relax the continuity constraint in the target functions and expand both the application domain and the stability of the approach. In this paper, we present a thorough analysis of the concept of stability condition of the generalized interpolant (the Lebesgue constant) by relating it to an inf-sup problem in the case of Hilbert spaces. In the second part of the paper, it will be explained how GEIM can be employed to monitor in real time physical experiments by providing an online accurate approximation of the phenomenon that is computed by combining the acquisition of a minimal number, optimally placed, measurements from the processes with their mathematical models (parameter-dependent PDEs). This idea is illustrated through a parameter dependent Stokes problem in which it is shown that the pressure and velocity fields can efficiently be reconstructed with a relatively low-dimensional interpolation space.},
+	journal = {Computer Methods in Applied Mechanics and Engineering},
+	author = {Maday, Y and Mula, O and Patera, A T and Yano, M},
+	year = {2015},
+	note = {Publisher: Elsevier B.V.},
+	keywords = {Model order reduction, Empirical interpolation, Generalized empirical interpolation, Reduced basis, Stability, Stokes equations},
+	pages = {310--334},
+}
+
+@article{introini_stabilization_2023,
+	title = {Stabilization of {Generalized} {Empirical} {Interpolation} {Method} ({GEIM}) in presence of noise: {A} novel approach based on {Tikhonov} regularization},
+	volume = {404},
+	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},
+	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},
+	year = {2023},
+	keywords = {GEIM, Data assimilation, Model order reduction, Noise stabilization, Tikhonov Regularization},
+	pages = {115773},
+}
+
+@article{maday_parameterized-background_2014,
+	title = {A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics},
+	volume = {102},
+	doi = {10.1002/nme.4747},
+	journal = {Int. J. Numer. Methods Eng.},
+	author = {Maday, Yvon and Patera, Anthony and Penn, James and Yano, Masayuki},
+	year = {2014},
+}
+
+@article{introini_non-intrusive_2023,
+	title = {Non-intrusive system state reconstruction from indirect measurements: {A} novel approach based on {Hybrid} {Data} {Assimilation} methods},
+	volume = {182},
+	copyright = {All rights reserved},
+	url = {https://www.sciencedirect.com/science/article/pii/S0306454922005680},
+	doi = {10.1016/j.anucene.2022.109538},
+	abstract = {The problem of estimating in real-time the state of a system by combining experimental data and models has been extensively addressed in literature. In particular, there have been a lot of developments in reduced order modelling techniques integrated in a data assimilation framework. This coupling allows to reconstruct the variable of interest considering a priori knowledge (i.e. the mathematical model) and some measurements of it. However, in some engineering systems not all the variables of interest may be measurable and hence the typical framework cannot be applied. However, these methods can be extended to reconstruct the full state of a system, by means of partial observations only. In this work, a novel approach will be introduced, based on a two step method: first the measurements are used to determine the parameters describing the system; then, the full state is estimated by means of reduced order modelling techniques. This new approach will be compared with the state-of-the-art both on a simple thermal hydraulics case and on an innovative nuclear reactor design, the Molten Salt Fast Reactor.},
+	journal = {Annals of Nuclear Energy},
+	author = {Introini, Carolina and Riva, Stefano and Lorenzi, Stefano and Cavalleri, Simone and Cammi, Antonio},
+	year = {2023},
+	keywords = {GEIM, Data assimilation, Indirect reconstruction, POD-I, Reduced order modelling},
+	pages = {109538--109538},
+}

joss-paper/paper.md

@@ -0,0 +1,50 @@
+---
+title: 'pyforce: Python Framework for data-driven model Order Reduction of multi-physiCs problEms'
+tags:
+  - Python
+  - reduced order modelling
+  - nuclear reactors
+  - data-driven
+  - multi physics
+authors:
+  - name: Stefano Riva
+    orcid: 0000-0001-9997-4101
+    equal-contrib: true
+    affiliation: 1 # (Multiple affiliations must be quoted "1, 2")
+  - name: Carolina Introini
+    orcid: 0000-0003-4682-1683
+    equal-contrib: true # (This is how you can denote equal contributions between multiple authors)
+    affiliation: 1
+  - name: Antonio Cammi
+    orcid: 0000-0003-1508-5935
+    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
+   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
+*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% }
+
+The techniques implemented here follow the same underlying idea expressed in Figure \autoref{fig:darom}: in the offline (training) phase, a dimensionality reduction process retrieves a reduced coordinate system onto which the information of the mathematical model is encoded; the sensor positioning algorithm then uses this reduced set to select the optimal location of sensors according to some optimality criterion, which depends on the adopted algorithm. In the online phase, the data assimilation process begins, retrieving a novel set of reduced variables and then computing the reconstructed state through a decoding step.
+
+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
+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
+
+This package aims to become a valuable tool for other researchers, engineers, and data scientists working in various fields where multi-physics problems play an important role, and its scope of application is not only restricted to the Nuclear Engineering world. The package also includes tutorials showing how to use the library and its main features, ranging from snapshot generation in dolfinx, import and mapping from OpenFOAM [@weller_tensorial_1998], to the offline and online phase of each of the aforementioned DDROM algorithms. The case studies are taken from the fluid dynamics and neutronics world, being the most important physics involved in nuclear reactor physics, although the methodologies can be extended to any physics of interest.
+
+# References