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Center for Data and Simulation Science

The main research interests of Janine Weber are the development and efficient implementation of hybrid methods that use machine learning algorithms to improve existing numerical methods and vice versa within the field of scientific machine learning (SciML). One exemplary application within this field is the development of robust and efficient adaptive domain decomposition methods for the iterative solution of heterogeneous problems, as, e.g., arising in solid mechanics. Here, dense feedforward neural networks are used to reduce the computational cost of the respective approach while still maintaining the robustness of the iterative solver. Additionally, Janine Weber is interested in the theoretical analysis and parallel implementation of efficient preconditioners that are highly parallel scalable on modern multi-core computers for the solution of large-scale problems. In particular, she works on adaptive, multi-level, and approximate domain decomposition methods, which scale up to many thousand of cores. Finally, Janine Weber is interested in the integration of new SciML approaches in high performance computing (HPC) software for modern computer architectures.

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Application of a feedforward neural network to predict the geometric location of adaptive coarse basis functions to setup a robust and efficient preconditioner for the computation of a dual-phase steel in solid mechanics.

Selected publications

  1. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber: "Machine Learning in Adaptive Domain Decomposition Methods - Predicting the Geometric Location of Constraints". SIAM J. Sci. Comput. 41 (2019), no. 6, A3887-A3912. https://doi.org/10.1137/18M1205364.
  2. Axel Klawonn, Martin Lanser, Oliver Rheinbach, Janine Weber: "Preconditioning the coarse problem of BDDC methods - Three-level, algebraic multigrid, and vertex-based preconditioners". Electronic Transaction on Numerical Analysis, 2019, Volume 51, pp. 432-450, 2019. https://doi.org/10.1553/etna_vol51s432.
  3. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber: "A Frugal FETI-DP and BDDC Coarse Space for Heterogeneous Problems". Electronic Transactions on Numerical Analysis (ETNA), Vol. 53, pp. 562-591, 2020. https://doi.org/10.1553/etna_vol53s562.
  4. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber: "Combining Machine Learning and Domain Decomposition Methods for the Solution of Partial Differential Equations - A Review". In GAMM Mitteilungen, 2021. https://doi.org/10.1002/gamm.202100001.
  5. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber: "Combining Machine Learning and Adaptive Coarse Spaces - A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions". SIAM J. Sci. Comput., 43(5):S816-S838, 2021. https://doi.org/10.1137/20M1344913.
  6. Viktor Grimm, Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber: "Estimating the time-dependent contact rate of SIR and SEIR models in mathematical epidemiology using physics-informed neural networks". Electronic Transactions on Numerical Analysis (ETNA), Volume 56, pp. 1–27, 2022. https://doi.org/10.1553/etna_vol56s1.
  7. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber: "Predicting the geometric location of critical edges in adaptive GDSW overlapping domain decomposition methods using deep learning". Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, Springer, Accepted for Publication, 2021. Preprint.
  8. Axel Klawonn, Martin Lanser, Janine Weber: "Learning Adaptive Coarse Basis Functions of FETI-DP". Submitted for Publication, 2022. Preprint.