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  1. Book ; Online: Feature Papers in Mathematical and Computational Applications

    Rozza, Gianluigi / Schütze, Oliver / Fantuzzi, Nicholas

    2023  

    Keywords Research & information: general ; Mathematics & science ; physics simulations ; neural networks ; electronic design ; heat equation ; error function ; function approximation ; spline approximation ; Gaussian function ; stochastic neural networks ; cell tracking ; microscopy image analysis ; detection-and-association methods ; image segmentation ; a priori segmentation ; level set method ; geodesic active contour ; computer simulation ; cardiovascular system ; parameterization ; validation ; animal model ; finite element method ; p-version ; harmonic extensions ; functional interpolation ; ordinary differential equations ; numerical methods ; microplastics ; Lotka-Volterra ; predator ; prey ; predator-prey ; pollution ; bioaccumulation ; biomagnification ; predation ; two-species model ; matrix sequences ; spectral analysis ; finite element approximations ; Darcy-Forchheimer model ; thermal radiation ; finite difference technique ; viscous dissipation ; Soret and Dufour impacts ; chemical reaction ; entropy generation ; agglomerated cork ; material modeling ; successive linear approximation ; finite element ; n/a
    Language English
    Size 1 electronic resource (240 pages)
    Publisher MDPI - Multidisciplinary Digital Publishing Institute
    Publishing place Basel
    Document type Book ; Online
    Note English
    HBZ-ID HT030722342
    ISBN 9783036567570 ; 3036567577
    Database ZB MED Catalogue: Medicine, Health, Nutrition, Environment, Agriculture

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  2. Book ; Online: Applications

    Schilders, Wil / Grivet-Talocia, Stefano / Benner, Peter / Quarteroni, Alfio / Rozza, Gianluigi / Silveira, Luís Miguel

    2021  

    Size 1 electronic resource (474 pages)
    Publisher De Gruyter
    Document type Book ; Online
    Note English ; Open Access
    HBZ-ID HT021027505
    ISBN 9783110499001 ; 3110499002
    Database ZB MED Catalogue: Medicine, Health, Nutrition, Environment, Agriculture

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  3. Book ; Online: Snapshot-Based Methods and Algorithms

    Schilders, Wil / Grivet-Talocia, Stefano / Benner, Peter / Quarteroni, Alfio / Rozza, Gianluigi / Silveira, Luís Miguel

    2021  

    Size 1 electronic resource (356 pages)
    Publisher De Gruyter
    Document type Book ; Online
    Note English ; Open Access
    HBZ-ID HT021026509
    ISBN 9783110671490 ; 3110671492
    Database ZB MED Catalogue: Medicine, Health, Nutrition, Environment, Agriculture

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  4. Book ; Online: System- and Data-Driven Methods and Algorithms

    Benner, Peter / Schilders, Wil / Grivet-Talocia, Stefano / Quarteroni, Alfio / Rozza, Gianluigi / Miguel Silveira, Luís

    2021  

    Keywords Numerical analysis ; Applied mathematics ; Mathematical physics ; Production engineering ; Computational physics ; Computer simulation
    Size 1 electronic resource (378 pages)
    Publisher De Gruyter
    Publishing place Berlin/Boston
    Document type Book ; Online
    Note English ; Open Access
    HBZ-ID HT021290079
    ISBN 9783110497717 ; 3110497719
    Database ZB MED Catalogue: Medicine, Health, Nutrition, Environment, Agriculture

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  5. Book ; Online: Model Order Reduction : Volume 3 Applications

    Benner, Peter / Schilders, Wil / Grivet-Talocia, Stefano / Quarteroni, Alfio / Rozza, Gianluigi / Miguel Silveira, Luís

    2020  

    Keywords Numerical analysis ; Applied mathematics ; Mathematical physics ; Production engineering ; Complexity reduction ; applications in engineering ; biomedical engineering ; computational physics ; computer science
    Size 1 electronic resource (466 pages)
    Publisher De Gruyter
    Publishing place Berlin/Boston
    Document type Book ; Online
    Note English ; Open Access
    HBZ-ID HT021027698
    ISBN 9783110499001 ; 3110499002
    Database ZB MED Catalogue: Medicine, Health, Nutrition, Environment, Agriculture

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  6. Book ; Online: Model Order Reduction : Volume 2: Snapshot-Based Methods and Algorithms

    Benner, Peter / Schilders, Wil / Grivet-Talocia, Stefano / Quarteroni, Alfio / Rozza, Gianluigi / Miguel Silveira, Luís

    2020  

    Keywords Numerical analysis ; Applied mathematics ; Mathematical physics ; Production engineering ; PROM
    Size 1 electronic resource (348 pages)
    Publisher De Gruyter
    Publishing place Berlin/Boston
    Document type Book ; Online
    Note English ; Open Access
    HBZ-ID HT021027608
    ISBN 9783110671490 ; 3110671492
    Database ZB MED Catalogue: Medicine, Health, Nutrition, Environment, Agriculture

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  7. Article ; Online: Generative adversarial reduced order modelling.

    Coscia, Dario / Demo, Nicola / Rozza, Gianluigi

    Scientific reports

    2024  Volume 14, Issue 1, Page(s) 3826

    Abstract: In this work, we present GAROM, a new approach for reduced order modeling (ROM) based on generative adversarial networks (GANs). GANs attempt to learn to generate data with the same statistics of the underlying distribution of a dataset, using two neural ...

    Abstract In this work, we present GAROM, a new approach for reduced order modeling (ROM) based on generative adversarial networks (GANs). GANs attempt to learn to generate data with the same statistics of the underlying distribution of a dataset, using two neural networks, namely discriminator and generator. While widely applied in many areas of deep learning, little research is done on their application for ROM, i.e. approximating a high-fidelity model with a simpler one. In this work, we combine the GAN and ROM framework, introducing a data-driven generative adversarial model able to learn solutions to parametric differential equations. In the presented methodology, the discriminator is modeled as an autoencoder, extracting relevant features of the input, and a conditioning mechanism is applied to the generator and discriminator networks specifying the differential equation parameters. We show how to apply our methodology for inference, provide experimental evidence of the model generalization, and perform a convergence study of the method.
    Language English
    Publishing date 2024-02-15
    Publishing country England
    Document type Journal Article
    ZDB-ID 2615211-3
    ISSN 2045-2322 ; 2045-2322
    ISSN (online) 2045-2322
    ISSN 2045-2322
    DOI 10.1038/s41598-024-54067-z
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  8. Book ; Online: Reduced order models for the buckling of hyperelastic beams

    Pichi, Federico / Rozza, Gianluigi

    2023  

    Abstract: In this paper, we discuss reduced order modelling approaches to bifurcating systems arising from continuum mechanics benchmarks. The investigation of the beam's deflection is a relevant topic of investigation with fundamental implications on their design ...

    Abstract In this paper, we discuss reduced order modelling approaches to bifurcating systems arising from continuum mechanics benchmarks. The investigation of the beam's deflection is a relevant topic of investigation with fundamental implications on their design for structural analysis and health. When the beams are exposed to external forces, their equilibrium state can undergo to a sudden variation. This happens when a compression, acting along the axial boundaries, exceeds a certain critical value. Linear elasticity models are not complex enough to capture the so-called beam's buckling, and nonlinear constitutive relations, as the hyperelastic laws, are required to investigate this behavior, whose mathematical counterpart is represented by bifurcating phenomena. The numerical analysis of the bifurcating modes and the post-buckling behavior, is usually unaffordable by means of standard high-fidelity techniques such (as the Finite Element method) and the efficiency of Reduced Order Models (ROMs), e.g.\ based on Proper Orthogonal Decomposition (POD), are necessary to obtain consistent speed-up in the reconstruction of the bifurcation diagram. The aim of this work is to provide insights regarding the application of POD-based ROMs for buckling phenomena occurring for 2-D and 3-D beams governed by different constitutive relations. The benchmarks will involve multi-parametric settings with geometrically parametrized domains, where the buckling's location depends on the material and geometrical properties induced by the parameter. Finally, we exploit the acquired notions from these toy problems, to simulate a real case scenario coming from the Norwegian petroleum industry.
    Keywords Mathematics - Numerical Analysis
    Subject code 621
    Publishing date 2023-05-31
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  9. Article: Model order reduction for bifurcating phenomena in fluid-structure interaction problems.

    Khamlich, Moaad / Pichi, Federico / Rozza, Gianluigi

    International journal for numerical methods in fluids

    2022  Volume 94, Issue 10, Page(s) 1611–1640

    Abstract: This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coandă effect, in a multi-physics setting involving fluid and solid media. Taking into consideration a fluid- ... ...

    Abstract This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coandă effect, in a multi-physics setting involving fluid and solid media. Taking into consideration a fluid-structure interaction problem, we aim at generalizing previous works towards a more reliable description of the physics involved. In particular, we provide several insights on how the introduction of an elastic structure influences the bifurcating behavior. We have addressed the computational burden by developing a reduced order branch-wise algorithm based on a monolithic proper orthogonal decomposition. We compared different constitutive relations for the solid, and we observed that a nonlinear hyper-elastic law delays the bifurcation w.r.t. the standard model, while the same effect is even magnified when considering linear elastic solid.
    Language English
    Publishing date 2022-06-04
    Publishing country England
    Document type Journal Article
    ZDB-ID 1491176-0
    ISSN 1097-0363 ; 0271-2091
    ISSN (online) 1097-0363
    ISSN 0271-2091
    DOI 10.1002/fld.5118
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  10. Article: Projection Based Semi-Implicit Partitioned Reduced Basis Method for Fluid-Structure Interaction Problems.

    Nonino, Monica / Ballarin, Francesco / Rozza, Gianluigi / Maday, Yvon

    Journal of scientific computing

    2022  Volume 94, Issue 1, Page(s) 4

    Abstract: In this manuscript a POD-Galerkin based Reduced Order Model for unsteady Fluid-Structure Interaction problems is presented. The model is based on a partitioned algorithm, with semi-implicit treatment of the coupling conditions. A Chorin-Temam projection ... ...

    Abstract In this manuscript a POD-Galerkin based Reduced Order Model for unsteady Fluid-Structure Interaction problems is presented. The model is based on a partitioned algorithm, with semi-implicit treatment of the coupling conditions. A Chorin-Temam projection scheme is applied to the incompressible Navier-Stokes problem, and a Robin coupling condition is used for the coupling between the fluid and the solid. The coupled problem is based on an Arbitrary Lagrangian Eulerian formulation, and the Proper Orthogonal Decomposition procedure is used for the generation of the reduced basis. We extend existing works on a segregated Reduced Order Model for Fluid-Structure Interaction to unsteady problems that couple an incompressible, Newtonian fluid with a linear elastic solid, in two spatial dimensions. We consider three test cases to assess the overall capabilities of the method: an unsteady, non-parametrized problem, a problem that presents a geometrical parametrization of the solid domain, and finally, a problem where a parametrization of the solid's shear modulus is taken into account.
    Language English
    Publishing date 2022-11-23
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2017260-6
    ISSN 1573-7691 ; 0885-7474
    ISSN (online) 1573-7691
    ISSN 0885-7474
    DOI 10.1007/s10915-022-02049-6
    Database MEDical Literature Analysis and Retrieval System OnLINE

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