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Description:
Model order reduction (MOR) is a technique to reduce the computational cost of high-dimensional models by approximating it with a low-dimensional surrogate model. Such techniques are required to evaluate high-dimensional models (a) many times (e.g. for parameter studies or optimization), (b) in real-time (e.g. for model-based control), or (c) on devices with low computational power (e.g. for embedded devices). Recently, techniques from machine learning have been investigated to enable MOR on manifolds, which can improve the approximation quality and broaden the applicability of MOR to problems that cannot be treated efficiently with the classical method.
In this project we develop a rigorous differential geometric framework for MOR on manifolds and use it to formulate structure-preserving MOR techniques. The derived surrogate models preserve desirable physical properties like the conservation of energy, which we use to guarantee stability and interpretability of the models.