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.

翻译：尽管作为保守现象的第一性原理模型无处不在，哈密顿系统即使在相对简单的线性情况下也面临着模型降阶的多重挑战。本文提出了一种基于投影的规范哈密顿系统模型降阶方法，该方法对于任意线性降维基的选择均保持变分一致性：哈密顿模型投影后仍为哈密顿模型。所提方法同时适用于侵入式与非侵入式场景，具有能量守恒与辛结构特性，其误差可严格分解为数据投影项与偏离规范形式的度量项。通过采用真实材料参数的线性弹性算例，本文展示了变分一致方法的优势：一致模型呈现稳定收敛，而以往依赖非一致技术或特殊设计基的方法则表现出不可接受的大误差。