• Corpus ID: 245353850

Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds

@article{Buchfink2021SymplecticMR,
  title={Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds},
  author={Patrick Buchfink and Silke Glas and Bernard Haasdonk},
  journal={ArXiv},
  year={2021},
  volume={abs/2112.10815}
}
Classical model reduction techniques project the governing equations onto linear subspaces of the high-dimensional state-space. For problems with slowly decaying Kolmogorov-nwidths such as certain transport-dominated problems, however, classical linear-subspace reducedorder models (ROMs) of low dimension might yield inaccurate results. Thus, the concept of classical linear-subspace ROMs has to be extended to more general concepts, like Model Order Reduction (MOR) on manifolds. Moreover, as we… 

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References

SHOWING 1-10 OF 61 REFERENCES
Rank-adaptive structure-preserving reduced basis methods for Hamiltonian systems
TLDR
This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena that demonstrates the superior stability properties and considerable runtime speedups of the proposed method as compared to global and traditional reduced basis approaches.
Structure Preserving Model Reduction of Parametric Hamiltonian Systems
TLDR
It is demonstrated that combining the greedy basis with the discrete empirical interpolation method also preserves the symplectic structure of Hamiltonian systems to ensure stability of the reduced model.
Hamiltonian Operator Inference: Physics-preserving Learning of Reduced-order Models for Hamiltonian Systems
TLDR
This work presents a nonintrusive physics-preserving method to learn reduced-order models (ROMs) of Hamiltonian systems that exploits knowledge of the Hamiltonian functional to define and parametrize a Hamiltonian ROM form which can be learned from data projected via symplectic projectors.
Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics
TLDR
This work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence and retains key properties such as energy conservation and symplectic time-evolution maps.
Symplectic Model Order Reduction with Non-Orthonormal Bases
Parametric high-fidelity simulations are of interest for a wide range of applications. However, the restriction of computational resources renders such models to be inapplicable in a real-time
Efficient nonlinear manifold reduced order model
TLDR
An efficient nonlinear manifold ROM (NM-ROM) is developed, which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs and shows that neural networks can learn a more efficient latent space representation on advection-dominated data from 2D Burgers' equations with a high Reynolds number.
Structure-Preserving Model Reduction for Nonlinear Port-Hamiltonian Systems
TLDR
A structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems that ensures the retention of port- Hamiltonian structure which assures the stability and passivity of the reduced model.
Projection-based model reduction with dynamically transformed modes
TLDR
A new model reduction framework for problems that exhibit transport phenomena that employs time-dependent transformation operators and generalizes MFEM to arbitrary basis functions is proposed, suitable to obtain a low-dimensional approximation with small errors even in situations where classical model order reduction techniques require much higher dimensions.
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