IC SimTech honors outstanding theses

December 17, 2020 / Sabine Sämisch

During its annual general meeting, the SimTech Industrial Consortium e V. has awarded Lena Scholz, Danny Driess and Timo Koch for their outstanding theses of 2019/2020. The winners that were selected by the IC SimTech board from all the nominations that were received briefly presented their works during the general meeting of IC SimTech. All three of them received a prize money of 500 Euros. The Industrial Consortium has awarded these prizes for the first time.

The winners are:

Lena Scholz, Bachelor student of Simulation Technology, for her bachelor thesis on “Effective heat transfer models in thin porous media“ (Jun.-Prof. Carina Bringedal, Prof. Rainer Helmig)

The aim of this thesis was to derive e_ective heat transfer models in a thin porous medium by using the approach of Homogenization. We have found upscaled equations to describe the uid velocity as well as the temperatures in the domain by using e_ective properties. The decisive advantage lies in the scale separation that is included in the model: The consideration of microscopic details in advance is incorporated in the relevant computations on the macroscopic scale by introducing these e_ective properties. This enables us to receive e_cient but reasonable results when dealing with porous media. By identifying e_ective quantities we are able to predict the properties of porous media on the macroscale since we can use microscopic insights without solving the upscaled equations. In this thesis I have focused on the e_ective heat conductivity in the porous medium. Since we have seen that the temperature related cell problem can be reduced to a two-dimensional equation set in case of Neumann boundary conditions in z-direction more exact solutions are possible through the usage of _ner grids. The presented results emphasize the dependence of the macroscopic behavior on small changes in the pore geometry and the microscopic structure. We have considered the impact of the grain's size and shape as well as the material properties of grain and uid. For speci_c cases such as layered media we obtain accurate results without solving the cell problem by using arithmetic and harmonic means. But in general it is necessary to solve the cell problem if exact results are needed. Several assumptions which are not applicable to all real-world applications have been used: Only thin periodic porous media have been considered. The cross-sectional shape of all grains is also expected to be identical and we do not allow changes of the pore geometry in z-direction or in time. In addition to that the case of a higher and therefore "-dependent P_eclet number has not been investigated here. Hence, the presented model is limited by these assumptions. Despite its limitations the model can be seen as a general basis for further extensions in order to incorporate more general settings.

Danny Driess, Master student of Simulation Technology, for his Master thesis on “A Machine Learning Approach to Control Musculoskeletal Systems” (Prof. Marc Toussaint, Prof. Syn Schmitt)

In this work, we propose a framework to learn an inverse model of redundant systems. We address three problems. By formalizing what it actually means to learn an inverse model, we derive a method where the inverse model, represented as a neural network, is learned by minimizing an upper bound on the real performance error, which is provided by a forward model (kernel regression or Gaussian process) learned on the currently available data. Most machine learning methods focus on learning the mapping of the function. For inverse models, it is, however, crucial to know the reachable set of the true forward model, since this becomes the domain of the inverse. Therefore, we secondly propose a method to estimate the reachable set of the system. Finally, we develop an active exploration strategy that is based on maximizing a lower bound on the true fill-distance to efficiently generate the data in the high dimensional input space. A key feature of our method is that the resulting learned inverse model provides error bounds on its performance. From an application point of view, this work is motivated by learning to control musculoskeletal systems. In the experiments, we show for both a simulated model of a human arm with six muscles and a real muscle-driven robot that the proposed method is able to learn the reachable set of these systems as well as a policy that enables to accurately control the position.

Timo Koch, former PhD student of the Graduate School of SimTech, for his doctoral thesis on “Mixed-dimension embedded models for flow and transport processes in porous media with embedded tubular network systems” (apl. Prof. Bernd Flemisch)

Flow in vascularized biological tissue, root water uptake, or flow around injection or extraction wells can be modeled by coupled mixed-dimensional PDE systems. Conceptually, such systems can be described as porous media with embedded tubular transport networks. We describe numerical methods for the simulation of such systems. The compartments are spatially discretized by non-matching computational grids: a three-dimensional mesh for the porous medium domain, and a geometrically embedded mesh of connected line segments for the network domain. A generalized abstract form of mixed-dimension embedded models is presented which summarizes several existing methods. A particularity of solutions to mixed-dimensional PDEs with dimensional gap two (0D-2D or 1D-3D) is the occurrence of singularities where the network center-lines intersect the porous domain. We introduce a new numerical scheme which removes these singularities by smoothing kernels, and exhibits improved convergence behavior and accuracy for coarse grid resolutions. The method is developed for isotropic, as well as anisotropic porous media. Furthermore, a new mixed-dimension embedded model for tissue perfusion and NMR signal generation is presented. Detailed perfusion simulations on the capillary scale are shown to reproduce image contrast of clinical (organ-scale) MRI data from multiple sclerosis patients. Similar modeling techniques and methods are then used to simulate root water uptake. For the implementation of such applications, a common software framework is developed by use of the open-source simulator \DuMuX The framework allows the implementation of coupled mixed- and equidimensional models in a unified way, using software abstractions. Possible framework applications go beyond the methods presented in this work.

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