STOCHASTIC GALERKIN METHOD AND PORT-HAMILTONIAN FORM FOR LINEAR FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS

We consider linear first -order systems of ordinary differential equations (ODEs) in port -Hamiltonian (pH) form. Physical parameters are remodeled 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 high -dimensional 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.