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Keywords: model order reduction; structure preservation; structural mechanics; data-driven reduction; large systems.
Organizers:
Saddam Hijazi (1) – saddam.hijazi@tu-braunschweig.de
Yevgeniya Filanova (2,3) – filanova@mpi-magdeburg.mpg.de
Affiliations:
(1) Technische Universität Braunschweig, Institute for Partial Differential Equations, Braunschweig, Germany
(2) Otto-von-Guericke University, Magdeburg, Germany
(3) Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
Abstract:
Real-world engineering applications are modeled by complex mathematical systems, usually resulting from the numerical discretization of PDEs/ODEs. The simulation of these systems is often a computationally demanding task, especially when considering time-dependent and three-dimensional problems. Model Order Reduction (MOR) stands out as a helpful tool that could mitigate the computational cost of running these numerical simulations, especially for the simulations with a large set of input parameters and configurations. The latter situation is common in many-query contexts such as optimization, optimal control, inverse problems, and data assimilation.
Model order reduction methods include classical intrusive methods based on the physics of the system, and non-intrusive methods based on data-driven and machine learning techniques. Both classes of methods have certain advantages and shortcomings. Intrusive MOR provides low-dimensional surrogate models with well-studied theoretical properties such as predictable error bounds, stability preservation, etc. In this case, access to the system matrices is required, which significantly limits the reduction of many structural mechanics simulations from modern software packages. On the other hand, non-intrusive methods allow the construction of reduced-order models only from the available input-output data. However, the cost of simulations to generate data and the difficulty of interpreting and validating the results must be considered. Each application problem requires analysis and selection of an appropriate MOR method to ensure effective reduction and optimal use of computational resources.
The goal of this mini-symposium is to discuss the practical benefits and limitations of both intrusive and non-intrusive model order reduction techniques in a variety of engineering and computational sciences.