Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces
ESAIM: M2AN, 54 6 (2020) 2159-2197
Published online: 2020-11-03
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Non-Intrusive Reduced Basis two-grid method for flow and transport problems in heterogeneous porous media
Wansheng Gao, Ludovic Chamoin and Insa NeuweilerJournal of Computational and Applied Mathematics 457 116321 (2025)
https://doi.org/10.1016/j.cam.2024.116321
A reduced-order model for advection-dominated problems based on the Radon Cumulative Distribution Transform
Tobias Long, Robert Barnett, Richard Jefferson-Loveday, Giovanni Stabile and Matteo IcardiAdvances in Computational Mathematics 51 (1) (2025)
https://doi.org/10.1007/s10444-024-10209-5
151 241 (2024)
https://doi.org/10.1007/978-3-031-55060-7_10
Nonlinear Reduced Order Modelling for Korteweg-de Vries Equation
Yusuf Çakır and Murat UzuncaInternational Journal of Informatics and Applied Mathematics 7 (1) 57 (2024)
https://doi.org/10.53508/ijiam.1455321
A graph convolutional autoencoder approach to model order reduction for parametrized PDEs
Federico Pichi, Beatriz Moya and Jan S. HesthavenJournal of Computational Physics 501 112762 (2024)
https://doi.org/10.1016/j.jcp.2024.112762
Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems
Junming Duan and Jan S. HesthavenJournal of Computational Physics 497 112621 (2024)
https://doi.org/10.1016/j.jcp.2023.112621
25 389 (2024)
https://doi.org/10.1016/bs.hna.2024.05.006
Data-driven snapshot calibration via monotonic feature matching
Neeraj Sarna, Jan Giesselmann and Peter BennerFinite Elements in Analysis and Design 230 104065 (2024)
https://doi.org/10.1016/j.finel.2023.104065
A Registration Method for Reduced Basis Problems Using Linear Optimal Transport
Tobias BlickhanSIAM Journal on Scientific Computing 46 (5) A3177 (2024)
https://doi.org/10.1137/23M1570715
Neural Galerkin schemes with active learning for high-dimensional evolution equations
Joan Bruna, Benjamin Peherstorfer and Eric Vanden-EijndenJournal of Computational Physics 496 112588 (2024)
https://doi.org/10.1016/j.jcp.2023.112588
Influence of sampling on the convergence rates of greedy algorithms for parameter-dependent random variables
Mohamed-Raed Blel, Virginie Ehrlacher and Tony LelièvreMathematics of Computation (2024)
https://doi.org/10.1090/mcom/3979
TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs
Yanlai Chen, Yajie Ji, Akil Narayan and Zhenli XuComputer Methods in Applied Mechanics and Engineering 430 117198 (2024)
https://doi.org/10.1016/j.cma.2024.117198
Hyper-reduction for parametrized transport dominated problems via adaptive reduced meshes
Sara Grundel and Neeraj SarnaPartial Differential Equations and Applications 5 (1) (2024)
https://doi.org/10.1007/s42985-023-00270-y
Structure-preserving reduced order model for parametric cross-diffusion systems
Jad Dabaghi and Virginie EhrlacherESAIM: Mathematical Modelling and Numerical Analysis 58 (3) 1201 (2024)
https://doi.org/10.1051/m2an/2024026
Learning to Generate Wasserstein Barycenters
Julien Lacombe, Julie Digne, Nicolas Courty and Nicolas BonneelJournal of Mathematical Imaging and Vision 65 (2) 354 (2023)
https://doi.org/10.1007/s10851-022-01121-y
Nonlinear approximation spaces for inverse problems
A. Cohen, M. Dolbeault, O. Mula and A. SomacalAnalysis and Applications 21 (01) 217 (2023)
https://doi.org/10.1142/S0219530522400140
Lookahead data-gathering strategies for online adaptive model reduction of transport-dominated problems
Rodrigo Singh, Wayne Isaac Tan Uy and Benjamin PeherstorferChaos: An Interdisciplinary Journal of Nonlinear Science 33 (11) (2023)
https://doi.org/10.1063/5.0169392
Model-order reduction for hyperbolic relaxation systems
Sara Grundel and Michael HertyInternational Journal of Nonlinear Sciences and Numerical Simulation 24 (7) 2763 (2023)
https://doi.org/10.1515/ijnsns-2021-0192
Manifold Approximations via Transported Subspaces: Model Reduction for Transport-Dominated Problems
Donsub Rim, Benjamin Peherstorfer and Kyle T. MandliSIAM Journal on Scientific Computing 45 (1) A170 (2023)
https://doi.org/10.1137/20M1316998
Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds and Approximation with Weakly Symplectic Autoencoder
Patrick Buchfink, Silke Glas and Bernard HaasdonkSIAM Journal on Scientific Computing 45 (2) A289 (2023)
https://doi.org/10.1137/21M1466657
Registration-based model reduction of parameterized two-dimensional conservation laws
Andrea Ferrero, Tommaso Taddei and Lei ZhangJournal of Computational Physics 457 111068 (2022)
https://doi.org/10.1016/j.jcp.2022.111068
State Estimation with Model Reduction and Shape Variability. Application to biomedical problems
Felipe Galarce, Damiano Lombardi and Olga MulaSIAM Journal on Scientific Computing 44 (3) B805 (2022)
https://doi.org/10.1137/21M1430480
Rank-adaptive structure-preserving model order reduction of Hamiltonian systems
Jan S. Hesthaven, Cecilia Pagliantini and Nicolò RipamontiESAIM: Mathematical Modelling and Numerical Analysis 56 (2) 617 (2022)
https://doi.org/10.1051/m2an/2022013
Mapping of coherent structures in parameterized flows by learning optimal transportation with Gaussian models
Angelo Iollo and Tommaso TaddeiJournal of Computational Physics 471 111671 (2022)
https://doi.org/10.1016/j.jcp.2022.111671
Linear/Ridge expansions: enhancing linear approximations by ridge functions
Constantin Greif, Philipp Junk and Karsten UrbanAdvances in Computational Mathematics 48 (3) (2022)
https://doi.org/10.1007/s10444-022-09936-4
Reduced basis methods for time-dependent problems
Jan S. Hesthaven, Cecilia Pagliantini and Gianluigi RozzaActa Numerica 31 265 (2022)
https://doi.org/10.1017/S0962492922000058
Numerical Mathematics and Advanced Applications ENUMATH 2019
H. Bansal, S. Rave, L. Iapichino, W. Schilders and N. van de WouwLecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications ENUMATH 2019 139 83 (2021)
https://doi.org/10.1007/978-3-030-55874-1_7
Structure-preserving reduced-order modeling of Korteweg–de Vries equation
Murat Uzunca, Bülent Karasözen and Süleyman YıldızMathematics and Computers in Simulation 188 193 (2021)
https://doi.org/10.1016/j.matcom.2021.03.042