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Optimal Transport–Inspired Deep Learning Framework for Slow-Decaying Kolmogorov \({n}\)-Width Problems: Exploiting Sinkhorn Loss and Wasserstein Kernel
Moaad Khamlich, Federico Pichi and Gianluigi Rozza SIAM Journal on Scientific Computing 47(2) C235 (2025) https://doi.org/10.1137/23M1604680
Optimal transport-based displacement interpolation with data augmentation for reduced order modeling of nonlinear dynamical systems
Moaad Khamlich, Federico Pichi, Michele Girfoglio, Annalisa Quaini and Gianluigi Rozza Journal of Computational Physics 531 113938 (2025) https://doi.org/10.1016/j.jcp.2025.113938
Model Order Reduction Using a Collocation Scheme on Chimera Meshes: Addressing the Kolmogorov \({N}\)-Width Barrier
Michel Bergmann, Michele Giuliano Carlino and Angelo Iollo SIAM Journal on Scientific Computing 47(4) A2272 (2025) https://doi.org/10.1137/24M1695099
Non-Intrusive Reduced Basis two-grid method for flow and transport problems in heterogeneous porous media
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 Icardi Advances in Computational Mathematics 51(1) (2025) https://doi.org/10.1007/s10444-024-10209-5
Nonlinear Reduced Order Modelling for Korteweg-de Vries Equation
Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds and Approximation with Weakly Symplectic Autoencoder
Patrick Buchfink, Silke Glas and Bernard Haasdonk SIAM Journal on Scientific Computing 45(2) A289 (2023) https://doi.org/10.1137/21M1466657
Lookahead data-gathering strategies for online adaptive model reduction of transport-dominated problems
Rodrigo Singh, Wayne Isaac Tan Uy and Benjamin Peherstorfer Chaos: An Interdisciplinary Journal of Nonlinear Science 33(11) (2023) https://doi.org/10.1063/5.0169392
Rank-adaptive structure-preserving model order reduction of Hamiltonian systems
Jan S. Hesthaven, Cecilia Pagliantini and Nicolò Ripamonti ESAIM: Mathematical Modelling and Numerical Analysis 56(2) 617 (2022) https://doi.org/10.1051/m2an/2022013
Linear/Ridge expansions: enhancing linear approximations by ridge functions
Numerical Mathematics and Advanced Applications ENUMATH 2019
H. Bansal, S. Rave, L. Iapichino, W. Schilders and N. van de Wouw Lecture 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