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Dynamical Approximation and Sensor Placement for Filtering Problems
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Friedrichs' systems discretized with the DGM: domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions
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
Nonlinear Embeddings for Conserving Hamiltonians and Other Quantities with Neural Galerkin Schemes
Paul Schwerdtner, Philipp Schulze, Jules Berman and Benjamin Peherstorfer SIAM Journal on Scientific Computing 46(5) C583 (2024) https://doi.org/10.1137/23M1607799
Optimization on the symplectic Stiefel manifold: SR decomposition-based retraction and applications
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
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
Energy-Conserving Hyper-Reduction and Temporal Localization for Reduced Order Models of the Incompressible Navier-Stokes Equations
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
A robust collision source method for rank adaptive dynamical low-rank approximation in radiation therapy