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Friedrichs' systems discretized with the DGM: domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions
Dynamical Approximation and Sensor Placement for Filtering Problems
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Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: a study using POD-Galerkin and dynamical low-rank approximation
Stochastic symplectic reduced-order modeling for model-form uncertainty quantification in molecular dynamics simulations in various statistical ensembles
Deep learning-based surrogate models for parametrized PDEs: Handling geometric variability through graph neural networks
Nicola Rares Franco, Stefania Fresca, Filippo Tombari and Andrea Manzoni Chaos: An Interdisciplinary Journal of Nonlinear Science 33(12) (2023) https://doi.org/10.1063/5.0170101
Energy-Conserving Hyper-Reduction and Temporal Localization for Reduced Order Models of the Incompressible Navier-Stokes Equations
Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds
Harsh Sharma, Hongliang Mu, Patrick Buchfink, Rudy Geelen, Silke Glas and Boris Kramer Computer Methods in Applied Mechanics and Engineering 417 116402 (2023) https://doi.org/10.1016/j.cma.2023.116402
Global energy preserving model reduction for multi-symplectic PDEs
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 dynamical low-rank integrators for first-order and second-order matrix differential equations