Variationally consistent Hamiltonian model reduction
<|reference_start|>Variationally consistent Hamiltonian model reduction: Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model reduction of canonical Hamiltonian systems that is variationally consistent for any choice of linear reduced basis: Hamiltonian models project to Hamiltonian models. Applicable in both intrusive and nonintrusive settings, the proposed method is energy-conserving and symplectic, with error provably decomposable into a data projection term and a term measuring deviation from canonical form. Examples from linear elasticity with realistic material parameters are used to demonstrate the advantages of a variationally consistent approach, highlighting the steady convergence exhibited by consistent models where previous methods reliant on inconsistent techniques or specially designed bases exhibit unacceptably large errors.<|reference_end|>
@article{gruber2024variationally,
    title={Variationally consistent Hamiltonian model reduction},
    author={Anthony Gruber, Irina Tezaur},
    journal={arXiv preprint arXiv:2404.15315},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.15315},
    primaryClass={math.NA cs.NA math.DS}
}