Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n-widths. Additionally, Hamiltonian structure of dynamical systems may be available and should be preserved during the reduction. In the current presentation, we address these two aspects by proposing a corresponding dictionary-based, online-adaptive MOR approach. The method requires dictionaries for the state-variable, non-linearities and discrete empirical interpolation (DEIM) points. During the online simulation, local basis extensions/simplifications are performed in an online-efficient way, i.e. the runtime complexity of basis modifications and online simulation of the reduced models do not depend on the full state dimension. Experiments on a linear wave equation and a non-linear Sine-Gordon example demonstrate the efficiency of the approach.

翻译：由于所需的投影基的规模较大，传统的参数问题模型降阶法（MOR）可能变得计算效率低下，特别是对于Kolmogorov n宽度缓慢衰减的问题更为如此。此外，动态系统的哈密顿结构可能是可用的，应该在缩减过程中予以保留。在本文中，我们通过提出相应的基于词典的在线自适应模型降阶方法来解决这两个方面的问题。该方法需要状态变量，非线性性和离散经验插值（DEIM）点的词典。在在线仿真期间，局部基扩展/简化是以在线高效的方式进行的，即基于修改和在线模拟的运行时复杂度不取决于完整状态维度。线性波动方程和非线性Sine-Gordon示例的实验表明了该方法的效率。