Variationally consistent Hamiltonian model reduction

TL;DR

This paper introduces a variationally consistent projection-based model reduction method for Hamiltonian systems that preserves energy and symplectic structure, improving accuracy and convergence over previous approaches.

Contribution

The authors develop a general, energy-conserving, symplectic model reduction technique for Hamiltonian systems that maintains variational consistency regardless of the basis choice.

Findings

Demonstrates steady convergence with the proposed method.

Shows advantages over previous inconsistent techniques.

Validates approach with linear elasticity examples.

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.