MOR-Seminar "Compatible Port-Hamiltonian Discretization and Model Reduction of a Nonlinear Flow Problem"

Structure-preserving approximation is still an active research area. By preserving or mimicking relevant geometric structures such as, e.g., conservation laws or symplecticities, unphysical solution behavior and numerical instabilities can be avoided in many cases. The model problem considered in this contribution describes nonlinear flows on networks. It covers a hierarchy of models used to describe gas network systems, including particularly the barotropic Euler equations. Our discretization and model reduction approach is analyzed using energy-based modeling concepts, such as the port-Hamiltonian formalism and the so-called partial Legendre-transformation. The latter offers an elegant approach for the systematic analysis of certain variable transformations, which widens the range of formulations, for which structure-preserving Galerkin-type approximations can be derived under a few compatibility conditions, using variational arguments only. A particular focus of the talk also lies on the realization of the snapshot-based model order- and complexity-reduction. While beneficial for the robustness and performance of the reduced models, the compatibility conditions pose a challenge in the training phase. Appropriate adaptions of the conventional model reduction methods will be presented.

Since 2009, this seminar represents a general platform for talks and exchange in the field of surrogate modelling, in particular Model Order Reduction (MOR) as well as novel data-based techniques in simulation science. Both methodological as well as application oriented presentations highlight the various aspects and the relevance of surrogate modelling in mathematics, technical mechanics, material science, control theory and other fields. We aim both at university members, as well as external persons from science and industry. The seminar is organized by four research groups and represents an activity of the SimTech Cluster of Excellence.

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