A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a straightforward linear solve given snapshot data and gray-box knowledge of the system Hamiltonian. Examples involving several hyperbolic partial differential equations show that the proposed method yields reduced models which, in addition to being accurate and stable with respect to the addition of basis modes, preserve conserved quantities well outside the range of their training data.

翻译：本文提出了一种用于正则与非正则哈密顿系统的非侵入式且保结构模型降阶方法。该方法基于算子推理思想，具有可证明的收敛性，在给定快照数据及系统哈密顿量的灰箱知识后，可简化为直接线性求解。涉及多个双曲型偏微分方程的算例表明，该方法生成的降阶模型不仅具有准确性及对基模增加保持稳定性，还能在训练数据范围之外良好地保持守恒量。