Dr. Hendrik Kleikamp
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
Research Foci
- Nonlinear model order reduction for transport-dominated problems
- Reduced basis methods and linear model order reduction
- Scientific machine learning (neural networks, kernel methods)
- (Optimal) Control of dynamical systems
Doctoral AbstractThesis
Parametrized optimal control and transport-dominated problems: Reduced basis methods, nonlinear reduction strategies and data driven surrogates
- Supervisors
- Doctoral Subject
- Mathematik
- Doctoral Degree
- Dr. rer. nat.
- Awarded by
- Department 10 – Mathematics and Computer Science
CV
Academic Education
- PhD in Mathematics
- MSc. Mathematics with Minor in Computer Science, Universität Münster
- BSc. Mathematics with Minor in Computer Science, Rheinische Friedrich-Wilhelms-Universität Bonn
Positions
- Scientific Assistant, Workgroup Ohlberger, Universität Münster
- Student Assistant, Institute for Analysis and Numerics, Universität Münster
- Student Assistant, Arithmeum, Rheinische Friedrich-Wilhelms-Universität Bonn
Teaching
- Lecture: Analysis und Numerik von Differentialgleichungen [100350]
(in cooperation with Julia Schleuß and Mario Ohlberger)
- Lecture: Model Order Reduction [108361]
(in cooperation with Stephan Rave) - Practical: Nichtlineare Modellierung in den Naturwissenschaften [108339]
(in cooperation with Julia Schleuß, Svetlana Gurevich, Andreas Heuer, Christian Engwer and Mario Ohlberger) - Practice: Übungen zu Model Order Reduction [108410]
(in cooperation with Stephan Rave)
- Lecture: Numerik Partieller Differentialgleichungen II [106353]
(in cooperation with Julia Schleuß and Mario Ohlberger)
- Lecture: Numerik partieller Differentialgleichungen [104495]
(in cooperation with Mario Ohlberger) - Practice: Übungen Numerik partieller Differentialgleichungen [104496]
(in cooperation with Mario Ohlberger)
- Lecture: Angewandte Funktionalanalysis [102399]
(in cooperation with Julia Schleuß and Mario Ohlberger) - Practice: Übungen zur Vorlesung Angewandte Funktionalanalysis [102400]
(in cooperation with Julia Schleuß and Mario Ohlberger)
- Lecture: Analysis und Numerik von Differentialgleichungen [100418]
(in cooperation with Mario Ohlberger) - Practical: Einführung in die Numerik mit Python [100378]
(in cooperation with Lukas Renelt and Mario Ohlberger) - Practice: Übungen zur Vorlesung: Analysis & Numerik von Differentialgleichungen [100388]
(in cooperation with Mario Ohlberger)
- Lecture: Numerical Optimization [108408]
(in cooperation with Mario Ohlberger) - Practice: Exercises to Numerical Optimization [108409]
(in cooperation with Mario Ohlberger)
- Lecture: Numerik partieller Differentialgleichungen [106352]
(in cooperation with Christian Engwer) - Practical: Nichtlineare Modellierung in den Naturwissenschaften [106351]
(in cooperation with Lukas Renelt, Julia Schleuß, André Schlichting, Svetlana Gurevich, Andreas Heuer, Christian Engwer and Mario Ohlberger)
- Practice: Übungen zu Numerik Partieller Differentialgleichungen II [104383]
(in cooperation with Mario Ohlberger)
- Practice: Übungen zu Inversen Problemen [102375]
(in cooperation with Frank Wübbeling)
Publications
- Kleikamp, Hendrik, and Renelt, Lukas. . “Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems.” Journal of Scientific Computing 104 (78). doi: 10.1007/s10915-025-02988-w.
- Kleikamp, Hendrik, Lazar, Martin, and Molinari, Cesare. . “Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems.” Preprint. ESAIM: Mathematical Modelling and Numerical Analysis 59 (1): 291–330. doi: 10.1051/m2an/2024074.
- Schembera, Björn, Wübbeling, Frank, Kleikamp, Hendrik, Schmidt, Burkhard, Shehu, Aurela, Reidelbach, Marco, Biedinger, Christine, Fiedler, Jochen, Koprucki, Thomas, Iglezakis, Dorothea, and Göddeke, Dominik. . “Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics.” in Proceedings of the 18th International Conference on Metadata and Semantics Research 2024, Communications in Computer and Information Science, edited by Michalis Sfakakis, Emmanouel Garoufallou, Matthew Damigos, Athena Salaba and Christos Papatheodorou. Cham: Springer. doi: 10.1007/978-3-031-81974-2_8.
- Kleikamp, Hendrik, and Ohlberger, Mario. . “Adaptive Model Hierarchies for Multi-Query Scenarios.” Preprint. in MATHMOD 2025 - Discussion Contribution Volume, edited by Andreas Körner, Andreas Kugi, Wolfgang Kemmetmüller, Andreas Deutschmann-Olek, Andreas Steinböck, Christian Hartl-Nesic and Lukasz Piotr Jadachowski. Wien: ARGESIM Verlag. doi: 10.34726/9007.
- Kleikamp, Hendrik, and Wenzel, Tizian. . “Kernel Methods in the Deep Ritz framework: Theory and practice.” Preprint. arXiv doi: 10.48550/arXiv.2410.03503.
- Kleikamp, Hendrik. . “Application of an adaptive model hierarchy to parametrized optimal control problems.” Preprint. in Proceedings of the Conference Algoritmy 2024, edited by P. Frolkovič and K.Mikula and D. Ševčovič. Bratislava: Jednota slovenských matematikov a fyzikov.
- Wenzel, Tizian, Haasdonk, Bernard, Kleikamp, Hendrik, Ohlberger, Mario, and Schindler, Felix. . “Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling.” Preprint. in Large-Scale Scientific Computations, Vol. 13952 of Lecture Notes in Computer Science, edited by I. Lirkov and S. Margenov. Cham: Springer Nature. doi: 10.1007/978-3-031-56208-2_11.
- Schembera, Björn, Wübbeling, Frank, Kleikamp, Hendrik, Biedinger, Christine, Fiedler, Jochen, Reidelbach, Marco, Shehu, Aurela, Schmidt, Burkhard, Koprucki, Thomas, Iglezakis, Dorothea, and Göddeke, Dominik. . “Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines.” in Metadata and Semantic Research - 17th Research Conference, MTSR 2023, Milan, Italy, October 25–27, 2023, Revised Selected Papers, Vol. 2048 of Communications in Computer and Information Science, edited by Emmanouel Garoufallou and Fabio Sartori. Cham: Springer. doi: 10.1007/978-3-031-65990-4_14.
- Haasdonk, B, Kleikamp, H, Ohlberger, M, Schindler, F, and Wenzel, T. . “A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs.” SIAM Journal on Scientific Computing 45 (3): A1039–1065. doi: 10.1137/22M1493318.
- Keil, T, Kleikamp, H, Lorentzen, R, Oguntola, M, and Ohlberger, M. . “Adaptive machine learning based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery.” Advances in Computational Mathematics 2022 (48) 73. doi: 10.1007/s10444-022-09981-z.
- Kleikamp, Hendrik, Ohlberger, Mario, and Rave, Stephan. . “Nonlinear Model Order Reduction using Diffeomorphic Transformations of a Space-Time Domain.” in MATHMOD 2022 - Discussion Contribution Volume, Vol. 17 of ARGESIM Report, edited by Felix Breitenecker, Wolfgang Kemmetmüller, Andreas Körner, Andreas Kugi and Inge Troch. Wien: ARGESIM Verlag. doi: 10.11128/arep.17.a17129.
Talks
Practical Talks
- Kleikamp, Hendrik : “Introduction to model order reduction for parametrized problems”. Work group meeting of the ON-DEM COST Action, Enschede, .
- Kleikamp, Hendrik : “Introduction to model order reduction for control systems”. Work group meeting of the ON-DEM COST Action, Enschede, .
Scientific Talks
- Kleikamp, Hendrik : “Model order reduction and machine learning for parametrized problems”. Seminar Talk, Graz, .
- Kleikamp, Hendrik : “Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems”. SIAM CSE (SIAM Conference on Computational Science and Engineering), Fort Worth, .
- Kleikamp, Hendrik : “Adaptive Model Hierarchies for Multi-Query Scenarios”. Minisymposium on "Recent Advances in Model Order Reduction and Data-driven Modelling" at MATHMOD (International Conference on Mathematical Modelling), Wien, .
- Kleikamp, Hendrik : “Model order reduction using nonlinear transformations of space-time domains”. Reisensburg Workshop on Nonlinear and Structure-Preserving Model Reduction, Günzburg, .
Practical Talk
- Kleikamp, Hendrik : “Reduced Basis Methods with pyMOR”. pyMOR School and User Meeting 2024, Münster, .
Scientific Talks
- Kleikamp, Hendrik : “Certified machine learning for model order reduction of parametrized problems”. Ulysseus Research Workshop on Mathematics in Machine Learning, Online, .
- Kleikamp, Hendrik : “Adaptive model hierarchies for solving parametrized optimal control problems in multi-query scenarios”. Seminar Talk, Genova, .
- Kleikamp, Hendrik : “Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems”. Minisymposium on "New Trends in Model Order Reduction and Learning" at ALGORITMY 2024, Central-European Conference on Scientific Computing, Podbanske, .
- Kleikamp, Hendrik : “Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems”. YMMOR - Young Mathematicians in Model Order Reduction, Stuttgart, .
Practical Talk
- Kleikamp, Hendrik : “Model order reduction with artificial neural networks in pyMOR”. Minitutorial on "pyMOR - Model Order Reduction with Python" at SIAM CSE (SIAM Conference on Computational Science and Engineering) 2023, Amsterdam, .
Scientific Talks
- Kleikamp, Hendrik : “Be greedy and learn - efficient and certified algorithms for parametrized optimal control problems”. Oberseminar Numerik, Münster, .
- Kleikamp, Hendrik : “A new Certified Hierarchical and Adaptive RB-ML-ROM Surrogate Model for Parametrized PDEs”. Minisymposium on "Adaptive Methods for Surrogate and Reduced Order Modeling" at ADMOS (XI International Conference on Adaptive Modeling and Simulation), Göteborg, .
- Kleikamp, Hendrik : “Nonlinear model order reduction for parametrized transport-dominated PDEs using registration-based methods”. YMMOR - Young Mathematicians in Model Order Reduction, Ulm, .
Practical Talk
- Kleikamp, Hendrik : “Model order reduction using artificial neural networks”. pyMOR School 2022, Magdeburg (online), .
Scientific Talks
- Kleikamp, Hendrik : “Nonlinear model order reduction for hyperbolic conservation laws by means of diffeomorphic transformations of space-time domains”. Model Reduction and Surrogate Modeling (MORE), Berlin, .
- Kleikamp, Hendrik : “Nonlinear model order reduction for parametrized hyperbolic conservation laws in a space-time domain”. Minisymposium on “Numerical methods for wave propagation problems” at CMAM (Computational Methods in Applied Mathematics) 2022, Wien, .
- Kleikamp, Hendrik : “Nonlinear Model Order Reduction using Diffeomorphic Transformations of a Space-Time Domain”. Minisymposium on "Recent Advances in Model Reduction and Surrogate Modeling" at MATHMOD (International Conference on Mathematical Modelling) 2022, Wien, .
- Kleikamp, Hendrik : “A certified and adaptive RB-ML-ROM surrogate approach for parametrized PDEs”. YMMOR - Young Mathematicians in Model Order Reduction, Münster, .
- Pelling, Art; Kleikamp, Hendrik : “Introduction to System Theory and Model Order Reduction”. YMMOR - Young Mathematicians in Model Order Reduction, Münster, .
- Kleikamp, Hendrik : “A certified and adaptive RB-ML-ROM surrogate approach for parametrized PDEs”. HCM Workshop: Synergies between Data Science and PDE Analysis, Bonn, .
- Kleikamp, Hendrik : “Nonlinear Model Order Reduction Using Geodesic Shooting in the Diffeomorphism Group”. Minisymposium on "Nonlinear Model Reduction Methods for Random or Parametric Time Dependent Problems" at SIAM UQ (SIAM Conference on Uncertainty Quantification) 2022, Atlanta, Georgia (hybrid), .
- Kleikamp, Hendrik : “Model order reduction using artificial neural networks”. pyMOR School 2021, Münster, .