Variationally consistent Hamiltonian model reduction
Abstract
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.
Cite
@article{arxiv.2404.15315,
title = {Variationally consistent Hamiltonian model reduction},
author = {Anthony Gruber and Irina Tezaur},
journal= {arXiv preprint arXiv:2404.15315},
year = {2024}
}