We consider linear first-order systems of ordinary differential equations (ODEs) in port-Hamiltonian (pH) form. Physical parameters are remodelled as random variables to conduct an uncertainty quantification. A stochastic Galerkin projection yields a larger deterministic system of ODEs, which does not exhibit a pH form in general. We apply transformations of the original systems such that the stochastic Galerkin projection becomes structure-preserving. Furthermore, we investigate meaning and properties of the Hamiltonian function belonging to the stochastic Galerkin system. A large number of random variables implies a highdimensional stochastic Galerkin system, which suggests itself to apply model order reduction (MOR) generating a low-dimensional system of ODEs. We discuss structure preservation in projection-based MOR, where the smaller systems of ODEs feature pH form again. Results of numerical computations are presented using two test examples.

翻译：我们考虑以端口-哈密顿（pH）形式表示的线性一阶常微分方程（ODEs）系统。将物理参数重新建模为随机变量以进行不确定性量化。随机伽辽金投影生成一个更大的确定性ODEs系统，但该系统通常不呈现pH形式。我们对原始系统进行变换，使得随机伽辽金投影能够保持结构。此外，我们研究了属于随机伽辽金系统的哈密顿函数的含义和性质。大量随机变量意味着高维的随机伽辽金系统，这自然促使应用模型降阶（MOR）生成低维ODEs系统。我们讨论了投影基MOR中的结构保持性问题，其中较小的ODEs系统再次呈现pH形式。通过两个测试实例展示了数值计算结果。