MOR-Seminar "Brain Networks, Gas Networks and Model Reduction"

Dynamic network behavior is a research object in various sciences and not least in applied mathematics: Network dynamics are studied in biological systems, such as the brain, in technical systems such as gas networks, or abstractly in neural networks. Realistic models of such large networks not only comprise a high dimensionality either due to a large number of nodes, or mathematical conditions such as hyperbolicity, but also due to complexities like (non-smooth) nonlinearities. Now, simulating network control or observations requires repeatedly solving a large-scale nonlinear dynamic system for many input or parameter configurations. Especially in time-constrained settings like short-term forecasts, the question if these simulations can be accelerated, arises. Data-driven system-theoretic model reduction is a remedy for this problem: A dynamic network model can be formulated as a (nonlinear) input-output system and based on the system-theoretic properties, which are approximated from simuations, a reduced order model can be computed. This approach is not unlike unsupervised learning, but instead of learning a surrogate model, rather its system-theoretic properties, and thereby its redundant and irrelevant components in terms of measurable input-output behavior, are obtained. A generic projection-based model order reduction framework for this approach is presented, together with a discussion of particular challenges and opportunities of neuronal brain networks and gas transport networks, as well as numerical examples alongside ideas for comparing reduced order models heuristically.

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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