publications | Stefano Riva

2025

arXiv
From Models To Experiments: Shallow Recurrent Decoder Networks on the DYNASTY Experimental Facility

Carolina Introini, Stefano Riva, J. Nathan Kutz, and 1 more author

Mar 2025

arXiv:2503.08907 [cs]

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The Shallow Recurrent Decoder networks are a novel paradigm recently introduced for state estimation, combining sparse observations with high-dimensional model data. This architecture features important advantages compared to standard data-driven methods including: the ability to use only three sensors (even randomly selected) for reconstructing the entire dynamics of a physical system; the ability to train on compressed data spanned by a reduced basis; the ability to measure a single field variable (easy to measure) and reconstruct coupled spatio-temporal fields that are not observable and minimal hyper-parameter tuning. This approach has been verified on different test cases within different fields including nuclear reactors, even though an application to a real experimental facility, adopting the employment of in-situ observed quantities, is missing. This work aims to fill this gap by applying the Shallow Recurrent Decoder architecture to the DYNASTY facility, built at Politecnico di Milano, which studies the natural circulation established by internally heated fluids for Generation IV applications, especially in the case of Circulating Fuel reactors. The RELAP5 code is used to generate the high-fidelity data, and temperature measurements extracted by the facility are used as input for the state estimation. The results of this work will provide a validation of the Shallow Recurrent Decoder architecture to engineering systems, showing the capabilities of this approach to provide and accurate state estimation.
@misc{introini_models_2025, title = {From {Models} {To} {Experiments}: {Shallow} {Recurrent} {Decoder} {Networks} on the {DYNASTY} {Experimental} {Facility}}, shorttitle = {From {Models} {To} {Experiments}}, url = {http://arxiv.org/abs/2503.08907}, doi = {10.48550/arXiv.2503.08907}, language = {en}, urldate = {2025-03-13}, publisher = {arXiv}, author = {Introini, Carolina and Riva, Stefano and Kutz, J. Nathan and Cammi, Antonio}, month = mar, year = {2025}, note = {arXiv:2503.08907 [cs]}, keywords = {Computer Science - Machine Learning, Physics - Computational Physics, Physics - Fluid Dynamics}, file = {PDF:/Users/sriva/Zotero/storage/LA7428IV/Introini et al. - 2025 - From Models To Experiments Shallow Recurrent Decoder Networks on the DYNASTY Experimental Facility.pdf:application/pdf} }
Towards Efficient Parametric State Estimation in Circulating Fuel Reactors with Shallow Recurrent Decoder Networks

Stefano Riva, Carolina Introini, J. Nathan Kutz, and 1 more author

Mar 2025

arXiv:2503.08904 [cs]

Abs DOI Bib

The recent developments in data-driven methods have paved the way to new methodologies to provide accurate state reconstruction of engineering systems; nuclear reactors represent particularly challenging applications for this task due to the complexity of the strongly coupled physics involved and the extremely harsh and hostile environments, especially for new technologies such as Generation-IV reactors. Data-driven techniques can combine different sources of information, including computational proxy models and local noisy measurements on the system, to robustly estimate the state. This work leverages the novel Shallow Recurrent Decoder architecture to infer the entire state vector (including neutron fluxes, precursors concentrations, temperature, pressure and velocity) of a reactor from three out-of-core time-series neutron flux measurements alone. In particular, this work extends the standard architecture to treat parametric time-series data, ensuring the possibility of investigating different accidental scenarios and showing the capabilities of this approach to provide an accurate state estimation in various operating conditions. This paper considers as a test case the Molten Salt Fast Reactor (MSFR), a Generation-IV reactor concept, characterised by strong coupling between the neutronics and the thermal hydraulics due to the liquid nature of the fuel. The promising results of this work are further strengthened by the possibility of quantifying the uncertainty associated with the state estimation, due to the considerably low training cost. The accurate reconstruction of every characteristic field in real-time makes this approach suitable for monitoring and control purposes in the framework of a reactor digital twin.
@misc{riva2025_parametricMSFR, title = {Towards {Efficient} {Parametric} {State} {Estimation} in {Circulating} {Fuel} {Reactors} with {Shallow} {Recurrent} {Decoder} {Networks}}, url = {http://arxiv.org/abs/2503.08904}, doi = {10.48550/arXiv.2503.08904}, language = {en}, urldate = {2025-03-13}, publisher = {arXiv}, month = mar, author = {Riva, Stefano and Introini, Carolina and Kutz, J. Nathan and Cammi, Antonio}, year = {2025}, abbrv = {arXiv}, note = {arXiv:2503.08904 [cs]}, keywords = {Computer Science - Computational Engineering, Finance, and Science, Computer Science - Machine Learning, Physics - Computational Physics}, annote = {Comment: arXiv admin note: text overlap with arXiv:2409.12550}, file = {PDF:/Users/sriva/Zotero/storage/E8T3KBPH/Riva et al. - 2025 - Towards Efficient Parametric State Estimation in Circulating Fuel Reactors with Shallow Recurrent De.pdf:application/pdf} }

2024

PoF
A finite element implementation of the incompressible Schrödinger flow method

Stefano Riva, Carolina Introini, and Antonio Cammi

Physics of Fluids, Jan 2024

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As first proposed by Madelung in 1926, the analogy between quantum mechanics and hydrodynamics has been known for a long time; however, its potentialities and the possibility of using the characteristic equations of quantum mechanics to simulate the behavior of inviscid fluids have not been thoroughly investigated in the past. In this methodology, the incompressible Euler equations are thus substituted by the Schrödinger equation, turning a quasi-linear Partial Differential Equation into a linear one, an algorithm known in the literature as Incompressible Schrödinger Flow. Previous works on the subject used the Fast Fourier Transform method to solve this problem, obtaining promising results, especially in predicting vortex dynamics; this paper aims to implement this novel approach into a Finite Element framework to find a more general formulation better suited for future application on complex geometries and on test cases closer to real-world applications. Simple case studies are presented in this work to analyze the potentialities of this method: the results obtained confirm that this method could potentially have some advantages over traditional Computational Fluid Dynamics method, especially for what concerns computational savings related to the required time discretization, whilst also introducing new aspects of the algorithm, mainly related to boundary conditions, not addressed in previous works.
@article{ISF_2023, author = {Riva, Stefano and Introini, Carolina and Cammi, Antonio}, title = {{A finite element implementation of the incompressible Schrödinger flow method}}, journal = {Physics of Fluids}, volume = {36}, number = {1}, pages = {017138}, year = {2024}, month = jan, issn = {1070-6631}, doi = {10.1063/5.0180356}, url = {https://doi.org/10.1063/5.0180356}, eprint = {https://pubs.aip.org/aip/pof/article-pdf/doi/10.1063/5.0180356/18930833/017138\_1\_5.0180356.pdf} }
NED
Data-driven model order reduction for sensor positioning and indirect reconstruction with noisy data: Application to a Circulating Fuel Reactor

Antonio Cammi, Stefano Riva, Carolina Introini, and 2 more authors

Nuclear Engineering and Design, May 2024

Abs DOI Bib

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{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}, month = may, url = {https://www.sciencedirect.com/science/article/pii/S002954932400205X}, author = {Cammi, Antonio and Riva, Stefano and Introini, Carolina and Loi, Lorenzo and Padovani, Enrico}, keywords = {Hybrid Data-Assimilation, Generalized Empirical Interpolation Method, Indirect Reconstruction, Sensors positioning, Molten Salt Fast Reactor, Noisy data} }
NED
OFELIA: An OpenMC-FEniCSx coupling for neutronic calculation with temperature feedback

Lorenzo Loi, Stefano Riva, Carolina Introini, and 3 more authors

Nuclear Engineering and Design, Nov 2024

Abs DOI Bib

The state of an operating nuclear reactor depends on several physical phenomena that coexist and are interdependent: they can be taken into account simultaneously by adopting a multi-physics approach, allowing a higher level of detail of the system’s properties. Neutron physics and thermal hydraulics are of great importance in this framework, their interdependence being the most fundamental coupling effect in nuclear reactors, as their interaction determines the power and temperature profiles, being quantities of interest during the design and safety analysis phases. This work focuses on developing a fully open-source multi-physics and multi-scale tool capable of determining the temperature profile of a characteristic fuel pin of a PWR when the power generated by the system is known. This methodology is implemented in a Python environment coupling the open source library FEniCSx for the thermal-hydraulic analysis with the OpenMC Monte Carlo code for the description of the fissionable system: regarding the former, FEniCSx handles the thermal calculations, whereas a 1D model is used to predict the axial coolant temperature distribution. The coupling applies an explicit method, whose convergence is based on a Picard scheme, using an adaptive relaxation scheme. This coupling strategy is compared with literature data, providing a good agreement with a fully Multi-Physics solver.
@article{LOI2024113480, title = {{OFELIA: An OpenMC-FEniCSx coupling for neutronic calculation with temperature feedback}}, journal = {Nuclear Engineering and Design}, volume = {428}, pages = {113480}, year = {2024}, issn = {0029-5493}, doi = {https://doi.org/10.1016/j.nucengdes.2024.113480}, month = nov, url = {https://www.sciencedirect.com/science/article/pii/S0029549324005806}, author = {Loi, Lorenzo and Riva, Stefano and Introini, Carolina and Giacobbo, Francesca and Wang, Xiang and Cammi, Antonio}, keywords = {OpenMC, FEniCSx, Nuclear reactor, Monte Carlo, Thermal hydraulics} }
AMM
Multi-physics model bias correction with data-driven reduced order techniques: Application to nuclear case studies

Stefano Riva, Carolina Introini, and Antonio Cammi

Applied Mathematical Modelling, Nov 2024

Abs DOI Bib

Due to the multiple physics involved and their mutual and complex interactions, nuclear engineers and researchers are constantly working on developing highly accurate Multi-Physics models, focusing in particular on the core coupling of Neutronics and Thermal-Hydraulics. Nevertheless, the development of accurate and stable models remains a challenging task despite the advancements in computational hardware and software. This work investigates the possibility of combining the available mathematical model with data collected on physical systems, with a two-fold goal: improvement of the performance of the former from the computational point of view without sacrificing accuracy and performing model bias correction with the knowledge coming in real-time from the system. In particular, two Data-Driven Reduced Order Modelling techniques, the Generalised Empirical Interpolation Method and the Parametrised-Background Data-Weak formulation, are applied to literature benchmark nuclear case studies, as they were observed to be quite well suited for the chosen cases. The main goal of this work is to assess the possibility of using external data to perform model bias correction: starting from a purposefully less accurate, but computationally cheaper base model, then using high-fidelity data to update and correct the model efficiently. Indeed, the numerical results obtained in this paper are promising, confirming the feasibility of this approach to develop computationally cheap and accurate multi-physics models; furthermore, investigation of Data-Driven Reduced Order Modelling approach to nuclear industrial cases, in the context of model bias correction, is foreseen.
@article{RIVA2024243, title = {Multi-physics model bias correction with data-driven reduced order techniques: Application to nuclear case studies}, journal = {Applied Mathematical Modelling}, volume = {135}, pages = {243-268}, year = {2024}, issn = {0307-904X}, doi = {https://doi.org/10.1016/j.apm.2024.06.040}, month = nov, url = {https://www.sciencedirect.com/science/article/pii/S0307904X24003196}, author = {Riva, Stefano and Introini, Carolina and Cammi, Antonio}, keywords = {Reduced order modelling, Data driven, Nuclear reactors, Multi-physics, Model correction} }
PoF
Application of a non-intrusive reduced order modeling approach to magnetohydrodynamics

M. Lo Verso, Stefano Riva, C. Introini, and 7 more authors

Physics of Fluids, Oct 2024

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Magnetohydrodynamics (MHD) investigates the intricate relationship between electromagnetism and fluid dynamics, offering a complete insight into the behavior of conducting fluids under the influence of magnetic fields. This theory plays a pivotal role in the framework of magnetic confinement fusion, where it can be applied to describe both thermonuclear plasmas confined inside the vacuum vessel and operating fluids, such as liquid metals and molten salts, flowing within the blanket of future tokamaks. Currently, the state-of-the-art numerical modeling of MHD scenarios employs a multi-physics framework to examine the interplay between magnetic fields and thermal hydraulics; however, due to the complexity of the involved physics, detailed models are required, resulting in a significant computational burden. In this regard, reduced order modeling (ROM) techniques may represent a promising solution, as they enable approximating complex systems with lower-dimensional models. Indeed, ROM methodologies can significantly reduce the required computational time while maintaining accuracy in capturing the convoluted physics involved in fusion reactors, especially in the contexts of sensitivity analysis, uncertainty quantification, and control. Despite their potential, ROM methods are relatively under-explored within the MHD framework; this study applies ROM techniques to MHD scenarios, focusing on their capabilities and possible limitations. To this aim, the backward-facing step, which is well suited for exploring the effects of different magnetic fields on turbulent dynamics, is adopted as case study. In particular, this work evaluates the potentialities of the ROM approach in enhancing computational efficiency within the MHD domain. Each of the methods evaluated was effective in precisely reconstructing flow dynamics at any given time and across the full range of magnetic field values tested while significantly reducing computational costs compared to full-order simulations. Practically, this study demonstrates the feasibility to create simplified models that accurately represent the magnetohydrodynamic flows of fluids within the blanket.
@article{MHD_ROM_2024, author = {Lo Verso, M. and Riva, Stefano and Introini, C. and Cervi, E. and Giacobbo, F. and Savoldi, L. and Di Prinzio, M. and Caramello, M. and Barucca, L. and Cammi, A.}, title = {{Application of a non-intrusive reduced order modeling approach to magnetohydrodynamics}}, journal = {Physics of Fluids}, volume = {36}, number = {10}, pages = {107167}, year = {2024}, month = oct, issn = {1070-6631}, doi = {10.1063/5.0230708}, url = {https://doi.org/10.1063/5.0230708}, eprint = {https://pubs.aip.org/aip/pof/article-pdf/doi/10.1063/5.0230708/20227612/107167\_1\_5.0230708.pdf} }

EPJWebConf

Impact of Malfunctioning Sensors on Data-Driven Reduced Order Modelling: Application to Molten Salt Reactors

Stefano Riva, Carolina Introini, Enrico Zio, and 1 more author

EPJ Web Conf., Oct 2024

DOI Bib

@article{SNAMC2024,
  author = {Riva, Stefano and Introini, Carolina and Zio, Enrico and Cammi, Antonio},
  title = {Impact of Malfunctioning Sensors on Data-Driven Reduced Order Modelling: Application to Molten Salt Reactors},
  doi = {10.1051/epjconf/202430217003},
  url = {https://doi.org/10.1051/epjconf/202430217003},
  journal = {EPJ Web Conf.},
  year = {2024},
  volume = {302},
  month = oct,
  pages = {17003}
}

JOSS

pyforce: Python Framework for data-driven model Order Reduction of multi-physiCs problEms

Stefano Riva, Carolina Introini, and Antonio Cammi

under review at Journal of Open Source Software, Jul 2024

DOI Bib

@article{pyforce2024,
  doi = {},
  url = {},
  year = {2024},
  publisher = {The Open Journal},
  volume = {},
  number = {},
  month = jul,
  pages = {},
  author = {Riva, Stefano and Introini, Carolina and Cammi, Antonio},
  title = {pyforce: Python Framework for data-driven model Order Reduction of multi-physiCs problEms},
  journal = {under review at Journal of Open Source Software},
}

SSRN

Enhancing Multi-Physics Modeling in New-Generation Nuclear Reactors Using Machine Learning: Implementing Gaussian Process Regression for Updating Cross Sections

Mahdi Aghili Nasr, Lorenzo Loi, Stefano Riva, and 3 more authors

under review to Annals of Nuclear Energy, Dec 2024

DOI Bib

@article{MSFR_GPR2024,
  title = {{Enhancing Multi-Physics Modeling in New-Generation Nuclear Reactors Using Machine Learning: Implementing Gaussian Process Regression for Updating Cross Sections}},
  journal = {under review to Annals of Nuclear Energy},
  volume = {},
  pages = {},
  year = {2024},
  month = dec,
  issn = {},
  doi = {10.2139/ssrn.5045576},
  url = {},
  author = {Nasr, Mahdi Aghili and Loi, Lorenzo and Riva, Stefano and Zolfaghari, AhmadReda and Wang, Xiang and Cammi, Antonio}
}

arXiv
Robust State Estimation from Partial Out-Core Measurements with Shallow Recurrent Decoder for Nuclear Reactors

Stefano Riva, Carolina Introini, Antonio Cammi, and 1 more author

Sep 2024

preprint available at \hrefhttps://arxiv.org/abs/2409.12550https://arxiv.org/abs/2409.12550

Abs DOI Bib

Reliable, real-time state estimation in nuclear reactors is of critical importance for monitoring, control and safety. It further empowers the development of digital twins that are sufficiently accurate for real-world deployment. As nuclear engineering systems are typically characterised by extreme environments, their in-core sensing is a challenging task, even more so in Generation-IV reactor concepts, which feature molten salt or liquid metals as thermal carriers. The emergence of data-driven methods allows for new techniques for accurate and robust estimation of the full state space vector characterising the reactor (mainly composed by neutron fluxes and the thermal-hydraulics fields). These techniques can combine different sources of information, including computational proxy models and local noisy measurements on the system, in order to robustly estimate the state. This work leverages the Shallow Recurrent Decoder (SHRED) architecture to estimate the entire state vector of a reactor from three, out-of-core time-series neutron flux measurements alone. Specifically, the Molten Salt Fast Reactor, in the EVOL geometry (Evaluation and Viability of Liquid Fuel Fast Reactor System project), is demonstrated as a test case, with neutron flux measurements alone allowing for reconstruction of the 20 coupled field variables of the dynamics. This approach can further quantify the uncertainty associated with the state estimation due to its considerably low training cost on compressed data. The accurate reconstruction of every characteristic field in real-time makes this approach suitable for monitoring and control purposes in the framework of a reactor digital twin.
@misc{riva2024robuststateestimationpartial, title = {Robust State Estimation from Partial Out-Core Measurements with Shallow Recurrent Decoder for Nuclear Reactors}, author = {Riva, Stefano and Introini, Carolina and Cammi, Antonio and Kutz, J. Nathan}, year = {2024}, eprint = {2409.12550}, journal = {under review to Progress in Nuclear Energy}, archiveprefix = {arXiv}, month = sep, primaryclass = {physics.ins-det}, doi = {10.48550/arXiv.2409.12550}, url = {https://arxiv.org/abs/2409.12550}, note = {preprint available at \href{https://arxiv.org/abs/2409.12550}{https://arxiv.org/abs/2409.12550}} }

PHYSOR24

Neutron Flux Reconstruction from Out-Core Sparse Measurements using Data-Driven Reduced Order Modelling

Stefano Riva, Sophie Deanesi, Carolina Introini, and 2 more authors

Apr 2024

DOI Bib

@inproceedings{PHYSOR24_MSFR_outcore,
  author = {Riva, Stefano and Deanesi, Sophie and Introini, Carolina and Lorenzi, Stefano and Cammi, Antonio},
  title = {Neutron Flux Reconstruction from Out-Core Sparse Measurements using Data-Driven Reduced Order Modelling},
  year = {2024},
  booktitle = {Proceedings of the International Conference on Physics of Reactors, PHYSOR 2024},
  pages = {1632 – 1641},
  month = apr,
  doi = {10.13182/PHYSOR24-43444},
  url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85202802833&doi=10.13182%2fPHYSOR24-43444&partnerID=40&md5=1c4a8e77492242e3a8ed39787b40f37d},
  type = {Conference paper},
  publication_stage = {Final},
  source = {Scopus}
}

PHYSOR24

An Alternative Approach for Group Constants Regression Based on Supervised Learning Techniques

Lorenzo Loi, Stefano Riva, Carolina Introini, and 3 more authors

Apr 2024

DOI Bib

@inproceedings{PHYSOR24_MC_ML,
  author = {Loi, Lorenzo and Riva, Stefano and Introini, Carolina and Padovani, Enrico and Giacobbo, Francesca and Cammi, Antonio},
  title = {An Alternative Approach for Group Constants Regression Based on Supervised Learning Techniques},
  year = {2024},
  booktitle = {Proceedings of the International Conference on Physics of Reactors, PHYSOR 2024},
  pages = {1674 – 1683},
  month = apr,
  doi = {10.13182/PHYSOR24-43521},
  url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85202868100&doi=10.13182%2fPHYSOR24-43521&partnerID=40&md5=0252a5766355b89b323a227b83256eb5},
  type = {Conference paper},
  publication_stage = {Final},
  source = {Scopus}
}

NENE2024

Shadowing Effect Correction for the Pavia TRIGA Reactor Using Monte Carlo Data and Reduced Order Modelling Techniques

Cyrille Ghislain De Lurion De L’Égouthail, Lorenzo Loi, Stefano Riva, and 2 more authors

In The 33rd International Conference Nuclear Energy for New Europe (NENE2024), Sep 2024

Bib

@inproceedings{NENE2024_Shadowing,
  title = {{Shadowing Effect Correction for the Pavia TRIGA Reactor Using Monte Carlo Data and Reduced Order Modelling Techniques}},
  author = {De Lurion De L'\'Egouthail, Cyrille Ghislain and Loi, Lorenzo and Riva, Stefano and Introini, Carolina and Cammi, Antonio},
  year = {2024},
  month = sep,
  booktitle = {The 33rd International Conference Nuclear Energy for New Europe (NENE2024)},
  address = {Portoroz, Slovenia},
  eventdate = {},
  isbn = {}
}

NENE2024

Analysis of KRUSTY reactor behaviour with OFELIA environment

Riccardo Boccelli, Lorenzo Loi, Stefano Riva, and 3 more authors

In The 33rd International Conference Nuclear Energy for New Europe (NENE2024), Sep 2024

Bib

@inproceedings{NENE2024_Ofelia4space,
  title = {{Analysis of KRUSTY reactor behaviour with OFELIA environment}},
  author = {Boccelli, Riccardo and Loi, Lorenzo and Riva, Stefano and Introini, Carolina and Lorenzi, Stefano and Cammi, Antonio},
  year = {2024},
  month = sep,
  booktitle = {The 33rd International Conference Nuclear Energy for New Europe (NENE2024)},
  address = {Portoroz, Slovenia},
  eventdate = {},
  isbn = {}
}

2023

CMAME
Stabilization of Generalized Empirical Interpolation Method (GEIM) in presence of noise: A novel approach based on Tikhonov regularization

Carolina Introini, Simone Cavalleri, Stefano Lorenzi, and 2 more authors

Computer Methods in Applied Mechanics and Engineering, Feb 2023

Abs DOI Bib

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”.
@article{TR_GEIM, title = {{Stabilization of Generalized Empirical Interpolation Method (GEIM) in presence of noise: A novel approach based on Tikhonov regularization}}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {404}, pages = {115773}, month = feb, year = {2023}, issn = {0045-7825}, doi = {https://doi.org/10.1016/j.cma.2022.115773}, url = {https://www.sciencedirect.com/science/article/pii/S0045782522007290}, author = {Introini, Carolina and Cavalleri, Simone and Lorenzi, Stefano and Riva, Stefano and Cammi, Antonio}, keywords = {GEIM, Tikhonov Regularization, Noise stabilization, Model order reduction, Data assimilation} }
ANE
Non-intrusive system state reconstruction from indirect measurements: A novel approach based on Hybrid Data Assimilation methods

Carolina Introini, Stefano Riva, Stefano Lorenzi, and 2 more authors

Annals of Nuclear Energy, Mar 2023

Abs DOI Bib

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.
@article{INTROINI2023109538, title = {Non-intrusive system state reconstruction from indirect measurements: A novel approach based on Hybrid Data Assimilation methods}, journal = {Annals of Nuclear Energy}, volume = {182}, pages = {109538}, year = {2023}, issn = {0306-4549}, month = mar, doi = {https://doi.org/10.1016/j.anucene.2022.109538}, url = {https://www.sciencedirect.com/science/article/pii/S0306454922005680}, author = {Introini, Carolina and Riva, Stefano and Lorenzi, Stefano and Cavalleri, Simone and Cammi, Antonio}, keywords = {Indirect reconstruction, GEIM, POD-I, Reduced order modelling, Data assimilation} }
ANE
Hybrid data assimilation methods, Part I: Numerical comparison between GEIM and PBDW

Stefano Riva, Carolina Introini, Stefano Lorenzi, and 1 more author

Annals of Nuclear Energy, Sep 2023

Abs DOI Bib

Hybrid Data Assimilation (HDA) methods are a class of numerical methods that aim at integrating Model Order Reduction (MOR) techniques into a Data Assimilation (DA) framework, thus combining mathematical models and experimental data. The objective is to reduce the solution time using MOR algorithms whilst keeping the accuracy of the models at the desired level using observations, which serve as an update to the a priori prediction of the model. This two-part work investigated HDA techniques by applying them to two classes of problems: numerical benchmark cases (part 1) and experimental facilities (part 2). In particular, this paper discusses the former, focusing on the numerical formulation of the methodologies and on the effect of noisy data. Indeed, real-world experimental data are always polluted by errors and uncertainties; therefore, it is critical to first assess the performance of these techniques on numerical benchmark cases with the artificial introduction of random noise before applying them to real-world experimental facilities. As such, this paper applies the Generalised Empirical Interpolation Method (GEIM) and the Parameterised-Background Data-Weak (PBDW) formulation to a non-adiabatic airflow over the classical computational fluid-dynamics benchmark of the 3D Backward Facing Step (BFS). Results show how both algorithms are valuable tools to reconstruct the state of the system when measurements are available, whilst assessing the effect of noise on the available data; in particular, the GEIM is a bit better than the PBDW since a lower reconstruction error is achieved with fewer sensors.
@article{RIVA2023109864, title = {{Hybrid data assimilation methods, Part I: Numerical comparison between GEIM and PBDW}}, journal = {Annals of Nuclear Energy}, volume = {190}, pages = {109864}, year = {2023}, month = sep, issn = {0306-4549}, doi = {https://doi.org/10.1016/j.anucene.2023.109864}, url = {https://www.sciencedirect.com/science/article/pii/S0306454923001834}, author = {Riva, Stefano and Introini, Carolina and Lorenzi, Stefano and Cammi, Antonio}, keywords = {GEIM, PBDW, Model order reduction, Data assimilation, Thermal hydraulics} }
ANE
Hybrid Data Assimilation methods, Part II: Application to the DYNASTY experimental facility

Stefano Riva, Carolina Introini, Stefano Lorenzi, and 1 more author

Annals of Nuclear Energy, Sep 2023

Abs DOI Bib

Hybrid Data Assimilation (HDA) methods aim at combining the advantages of mathematical models and experimental observations by integrating Model Order Reduction techniques into a Data Assimilation framework, thus reducing the solution time whilst keeping the accuracy of the models to the desired level. HDA methods provide tools able to estimate the state of a system assuming to have measurements available per each field describing the system (e.g., neutron flux, temperature, velocity, …). However, it is not always possible to measure every field of interest for various reasons, thus these techniques should be adapted: in particular, it is legitimate to investigate the possibility of extracting some information from indirect measurement. Following the assessment of the two selected HDA methods (Generalised Empirical Interpolation Method and Parameterised Background Data-Weak) performed on a numerical benchmark test case discussed in the first part of this two-part work, the present paper now deals with their testing on a real-world experimental facility and their validation with experimental data. This work represents the first step for a deep validation phase to assess their efficiency and reliability, applying the Generalised Empirical Interpolation Method (GEIM), the Parameterised-Background Data-Weak (PBDW) formulation and the Indirect Reconstruction (IR) algorithm to DYNASTY, an experimental facility for studying natural circulation built at Politecnico di Milano. The robustness of these methods is high when the models are accurate, however when real system are analysed the model discrepancy can be present and these techniques may suffer.
@article{RIVA2023109863, title = {{Hybrid Data Assimilation methods, Part II: Application to the DYNASTY experimental facility}}, journal = {Annals of Nuclear Energy}, volume = {190}, pages = {109863}, year = {2023}, issn = {0306-4549}, doi = {https://doi.org/10.1016/j.anucene.2023.109863}, month = sep, url = {https://www.sciencedirect.com/science/article/pii/S0306454923001822}, author = {Riva, Stefano and Introini, Carolina and Lorenzi, Stefano and Cammi, Antonio}, keywords = {GEIM, PBDW, Indirect Reconstruction, Model Order Reduction, Data Assimilation, DYNASTY} }

ICAPP2023

Indirect Field Reconstruction and Sensor Positioning in Circulating Fuel Reactors using Data-Driven Model Order Reduction

Antonio Cammi, Stefano Riva, Carolina Introini, and 2 more authors

In 2023 International Congress on Advances in Nuclear Power Plants, Apr 2023

Bib

@inproceedings{ICAPP2023,
  title = {{Indirect Field Reconstruction and Sensor Positioning in Circulating Fuel Reactors using Data-Driven Model Order Reduction}},
  author = {Cammi, Antonio and Riva, Stefano and Introini, Carolina and Loi, Lorenzo and Padovani, Enrico},
  year = {2023},
  month = apr,
  booktitle = {2023 International Congress on Advances in Nuclear Power Plants},
  address = {Gyeongju, Korea},
  eventdate = {2023-04-23/2023-04-27},
  isbn = {979-11-955566-5-6}
}

NENE2023

Multi-Physics Model Correction with Data-Driven Reduced Order Modelling

Stefano Riva, Carolina Introini, and Antonio Cammi

In 32nd International Conference Nuclear Energy for New Europe (NENE2023), Sep 2023

Bib

@inproceedings{NENE2023_RMP,
  title = {{Multi-Physics Model Correction with Data-Driven Reduced Order Modelling}},
  author = {Riva, Stefano and Introini, Carolina and Cammi, Antonio},
  year = {2023},
  month = sep,
  booktitle = {32nd International Conference Nuclear Energy for New Europe (NENE2023)},
  address = {Portoroz, Slovenia},
  eventdate = {2023-09-11/2023-09-14},
  isbn = {978-961-6207-56-0}
}

NENE2023

FEniCSx-OpenMC Coupling for Neutronic Calculation with Temperature Feedback

Stefano Riva, Lorenzo Loi, Carolina Introini, and 2 more authors

In 32nd International Conference Nuclear Energy for New Europe (NENE2023), Sep 2023

Bib

@inproceedings{NENE2023_FenicsOpenMC,
  title = {{FEniCSx-OpenMC Coupling for Neutronic Calculation with Temperature Feedback}},
  author = {Riva, Stefano and Loi, Lorenzo and Introini, Carolina and Cammi, Antonio and Wang, Xiang},
  year = {2023},
  month = sep,
  booktitle = {32nd International Conference Nuclear Energy for New Europe (NENE2023)},
  address = {Portoroz, Slovenia},
  eventdate = {2023-09-11/2023-09-14},
  isbn = {978-961-6207-56-0}
}

NENE2023

OpenMC Analysis of TRIGA Mark II Reactor Void and Temperature Reactivity Coefficients

Lorenzo Loi, Stefano Riva, Carolina Introini, and 2 more authors

In 32nd International Conference Nuclear Energy for New Europe (NENE2023), Sep 2023

Bib

@inproceedings{NENE2023_OpenMC_Void,
  title = {{OpenMC Analysis of TRIGA Mark II Reactor Void and Temperature Reactivity Coefficients}},
  author = {Loi, Lorenzo and Riva, Stefano and Introini, Carolina and Cammi, Antonio and Padovani, Enrico},
  year = {2023},
  month = sep,
  booktitle = {32nd International Conference Nuclear Energy for New Europe (NENE2023)},
  address = {Portoroz, Slovenia},
  eventdate = {2023-09-11/2023-09-14},
  isbn = {978-961-6207-56-0}
}

2022

NENE2022

Inviscid Fluid Simulation through \textitIncompressible Schrödinger Flow: a Finite Element approach

Stefano Riva, Antonio Cammi, and Carolina Introini

In 31st International Conference Nuclear Energy for New Europe (NENE2022), Sep 2022

Bib

@inproceedings{NENE2022_Schrodinger,
  title = {{Inviscid Fluid Simulation through \textit{Incompressible Schr{\"o}dinger Flow}: a Finite Element approach}},
  author = {Riva, Stefano and Cammi, Antonio and Introini, Carolina},
  year = {2022},
  month = sep,
  booktitle = {31st International Conference Nuclear Energy for New Europe (NENE2022)},
  address = {Portoroz, Slovenia},
  eventdate = {2022-09-12/2022-09-15},
  isbn = {978-961-6207-53-9}
}