08 Fakultät Mathematik und Physik

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9

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Institute: search.filters.UBSInstitut.Fakultätsübergreifend / Sonstige EinrichtungAuthor: search.filters.author.Buchfink, Patrick

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    Symplectic model order reduction with non-orthonormal bases
    (2019) Buchfink, Patrick; Bhatt, Ashish; Haasdonk, Bernard
    Parametric high-fidelity simulations are of interest for a wide range of applications. But the restriction of computational resources renders such models to be inapplicable in a real-time context or in multi-query scenarios. Model order reduction (MOR) is used to tackle this issue. Recently, MOR is extended to preserve specific structures of the model throughout the reduction, e.g. structure-preserving MOR for Hamiltonian systems. This is referred to as symplectic MOR. It is based on the classical projection-based MOR and uses a symplectic reduced order basis (ROB). Such a ROB can be derived in a data-driven manner with the Proper Symplectic Decomposition (PSD) in the form of a minimization problem. Due to the strong nonlinearity of the minimization problem, it is unclear how to efficiently find a global optimum. In our paper, we show that current solution procedures almost exclusively yield suboptimal solutions by restricting to orthonormal ROBs. As new methodological contribution, we propose a new method which eliminates this restriction by generating non-orthonormal ROBs. In the numerical experiments, we examine the different techniques for a classical linear elasticity problem and observe that the non-orthonormal technique proposed in this paper shows superior results with respect to the error introduced by the reduction.
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    Greedy kernel methods for approximating breakthrough curves for reactive flow from 3D porous geometry data
    (2024) Herkert, Robin; Buchfink, Patrick; Wenzel, Tizian; Haasdonk, Bernard; Toktaliev, Pavel; Iliev, Oleg
    We address the challenging application of 3D pore scale reactive flow under varying geometry parameters. The task is to predict time-dependent integral quantities, i.e., breakthrough curves, from the given geometries. As the 3D reactive flow simulation is highly complex and computationally expensive, we are interested in data-based surrogates that can give a rapid prediction of the target quantities of interest. This setting is an example of an application with scarce data, i.e., only having a few available data samples, while the input and output dimensions are high. In this scarce data setting, standard machine learning methods are likely to fail. Therefore, we resort to greedy kernel approximation schemes that have shown to be efficient meshless approximation techniques for multivariate functions. We demonstrate that such methods can efficiently be used in the high-dimensional input/output case under scarce data. Especially, we show that the vectorial kernel orthogonal greedy approximation (VKOGA) procedure with a data-adapted two-layer kernel yields excellent predictors for learning from 3D geometry voxel data via both morphological descriptors or principal component analysis.