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Publications on Scientific Machine Learning
 

  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. Preprint and https://doi.org/10.1137/18M1205364.
  2. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber, "Machine Learning in Adaptive FETI-DP - A Comparison of Smart and Random Training Data". Domain Decomposition Methods in Science and Engineering XXV. DD 2018. Lecture Notes in Computational Science and Engineering, vol 138. Springer, Cham, 2020. https://doi.org/10.1007/978-3-030-56750-7_24, Preprint.
  3. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Machine Learning in Adaptive FETI-DP - Reducing the Effort in Sampling". Proceedings of the ENUMATH 2019 conference, Springer LNCSE, Vol. 139, pp. 593-603, 2021. Preprint.
  4. Matthias Eichinger, Alexander Heinlein, Axel Klawonn. "Stationary flow predictions using convolutional neural networks". Proceedings of the ENUMATH 2019 conference, Springer LNCSE, Vol. 139, pp. 541-549, 2021. Preprint.
  5. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Combining Machine Learning and Domain Decomposition Methods - A Review". In GAMM Mitteilungen, 2021. Preprint and https://onlinelibrary.wiley.com/doi/full/10.1002/gamm.202100001
  6. 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., Special Section Copper Mountain 2020, published 2021. Preprint, https://doi.org/10.1137/20M1344913.
  7. 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. http://doi.org/10.1553/etna_vol56s1, Preprint.
  8. Matthias Eichinger, Alexander Heinlein, Axel Klawonn. "Surrogate Convolutional Neural Network Models for Steady Computational Fluid Dynamics Simulations". Electronic Transactions on Numerical Analysis (ETNA), Vol. 56, pp. 235-255, 2022. http://doi.org/10.1553/etna_vol56s235​​​​​​​, Preprint.
  9. 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, vol 145. Springer, 2023. https://link.springer.com/chapter/10.1007/978-3-030-95025-5_32, Preprint.
  10. Axel Klawonn, Martin Lanser, Janine Weber, "Learning Adaptive Coarse Basis Functions of FETI-DP". Journal of Computational Physics, Vol 496, Elsevier, 2023. https://doi.org/10.1016/j.jcp.2023.112587, Preprint.
  11. Axel Klawonn, Martin Lanser, Janine Weber, "Learning Adaptive FETI-DP Constraints for Irregular Domain Decompositions". Domain Decomposition Methods in Science and Engineering XXVII. Lecture Notes in Computational Science and Engineering, vol 149. Springer, 2024. https://link.springer.com/chapter/10.1007/978-3-031-50769-4_33, Preprint.
  12. Viktor Grimm, Alexander Heinlein, Axel Klawonn, "A short note on solving partial differential equations using convolutional neural networks". v. Lecture Notes in Computational Science and Engineering, vol 149. Springer, 2024.​​​​​​​​​​​​​​​​​​ https://link.springer.com/chapter/10.1007/978-3-031-50769-4_1,​​​ Preprint.​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  13. Axel Klawonn, Martin Lanser, Janine Weber, "A Domain Decomposition-Based CNN-DNN Architecture for Model Parallel Training Applied to Image Recognition Problems". SIAM J. Sci. Comput, Vol 46(5), 2024. https://doi.org/10.1137/23M1562202, https://arxiv.org/abs/2302.06564
  14. Axel Klawonn, Martin Lanser, Janine Weber, "Machine learning and domain decomposition methods - a survey". Comput. Sci. Eng., Springer, 2024. https://link.springer.com/article/10.1007/s44207-024-00003-y, Preprint.​​​​​​​
  15. Axel Klawonn, Martin Lanser, Lucas Mager, Ameya Rege, “Computational homogenization for aerogel-like polydisperse open-porous materials using neural network--based surrogate models on the microscale”, Computational Mechanics, Springer, Vol. 77, pages 297 - 317, 2025. https://link.springer.com/article/10.1007/s00466-024-02588-9, Preprint.
  16. Viktor Grimm, Alexander Heinlein, Axel Klawonn, "Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks". Journal of Computational Physics, vol 535, Elsevier, 2025, https://doi.org/10.1016/j.jcp.2025.114027.
  17. Axel Klawonn, Martin Lanser, Janine Weber, "Learning Adaptive Constraints in Nonlinear FETI-DP Methods". Proceedings of the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) 2023, Volume 2, Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-86169-7_5, Preprint.​​​​​​​​​​​​​​
  18. Dinesh Parthasarathy, Tommaso Bevilacqua, Martin Lanser, Axel Klawonn, Harald Köstler, “Towards Automated Algebraic Multigrid Preconditioner Design Using Genetic Programming for Large-Scale Laser Beam Welding Simulations”. Proceedings of the Platform for Advanced Scientific Computing Conference (PASC 2025), 2025. https://doi.org/10.1145/3732775.3733589, Preprint.
  19. Axel Klawonn, Martin Lanser, Janine Weber-Hamacher, “Domain-Decomposed Image Classification Algorithms Using Linear Discriminant Analysis and Convolutional Neural Networks”. In: Pichi, F., Rozza, G., Strazzullo, M., Torlo, D. (eds) Scientific Machine Learning. SMLET 2024. SEMA SIMAI Springer Series, vol 42. Springer, Cham., 2026, https://doi.org/10.1007/978-3-032-11527-0_1

If your institution is not a subscriber to the corresponding journals, the links to the articles might not work. In this case, please contact the author for a hardcopy. axel.klawonn(at)uni-koeln(dot)de

Accepted for publication

  1. Axel Klawonn, Martin Lanser, Janine Weber, "Model Parallel Training and Transfer Learning for Convolutional Neural Networks by Domain Decomposition". Accepted for publication in the Proceedings of the Conference on Domain Decomposition Methods in Science and Engineering XXVIII, 2025. Preprint.
  2. Simon Klaes, Axel Klawonn, Natalie Kubicki, Martin Lanser, Kengo Nakajima, Takashi Shimokawabe, Janine Weber-Hamacher, “A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations”, Submitted for publication in 2025, accepted for publication in SIAM J. Sci. Comput., 2026. Preprint.

Submitted for publication

  1. Axel Klawonn, Martin Lanser, Janine Weber-Hamacher, "Learning Adaptive Coarse Spaces Using Transferable Neural Network Models for Linear and Nonlinear Overlapping Domain Decomposition Methods". Submitted for publication, 2026. Preprint.