Patrick Gelß

My main area of focus lies in the development and application of quantum- and tensor-based methods. These methodologies have proven to be incredibly effective in solving complex problems across a range of fields. In addition to this, I have a strong interest in various topics in the fields of machine learning and data-driven approaches, kernel-based techniques, dynamical systems and transfer operators, catalytic systems, chemical reaction networks, and quantum mechanics, including quantum computing and simulation.

📬 Contact

office
Room 1356 at ZIB
e-mail
homepage
patrickgelss.com
languages
German and English

🎓 Curriculum vitae

since 2022
Researcher at ZIB
2021 to 2022
Researcher at FUB
2020 to 2020
Researcher at ZIB
2017 to 2020
Researcher at FUB
Jun 2017
Ph.D. in Applied Mathematics at FUB
Oct 2013
Diploma in Mathematics at FUB

📝 Publications and preprints

Preprints

  1. Gelß, P., Klein, R., Matera, S., and Schmidt, B. (2023). Quantum Dynamics of Coupled Excitons and Phonons in Chain-like Systems: Tensor Train Approaches and Higher-order Propagators. [arXiv]
    [BibTeX]
    @misc{2023_GelssKleinMateraSchmidt_QuantumdynamicsTensortrain,
      archiveprefix = {arXiv},
      eprint = {2302.03568},
      primaryclass = {quant-ph},
      year = {2023},
      author = {Gelß, Patrick and Klein, Rupert and Matera, Sebastian and Schmidt, Burkhard},
      title = {Quantum Dynamics of Coupled Excitons and Phonons in Chain-like Systems: Tensor Train Approaches and Higher-order Propagators}
    }
  2. Klus, S., and Gelß, P. (2023). Continuous Optimization Methods for the Graph Isomorphism Problem. [arXiv]
    [BibTeX]
    @misc{2023_KlusGelss_Continuousgraphisomorphism,
      archiveprefix = {arXiv},
      eprint = {2311.16912},
      primaryclass = {cs.DM},
      year = {2023},
      author = {Klus, Stefan and Gelß, Patrick},
      title = {Continuous Optimization Methods for the Graph Isomorphism Problem}
    }
  3. Gelß, P., Klus, S., Knebel, S., Shakibaei, Z., and Pokutta, S. (2022). Low-rank Tensor Decompositions of Quantum Circuits. [arXiv]
    [BibTeX]
    @misc{2022_GelssKlusShakibaeiPokutta_Lowranktensordecompositions,
      archiveprefix = {arXiv},
      eprint = {2205.09882},
      primaryclass = {quant-ph},
      year = {2022},
      author = {Gelß, Patrick and Klus, Stefan and Knebel, Sebastian and Shakibaei, Zarin and Pokutta, Sebastian},
      title = {Low-rank Tensor Decompositions of Quantum Circuits}
    }
  4. Gelß, P., and Schütte, C. (2018). Tensor-generated Fractals - Using Tensor Decompositions for Creating Self-similar Patterns. [arXiv]
    [BibTeX]
    @misc{2018_GelssSchuette_Tensorfractals,
      archiveprefix = {arXiv},
      eprint = {1812.00814},
      primaryclass = {math.GM},
      year = {2018},
      author = {Gelß, Patrick and Schütte, Christof},
      title = {Tensor-generated Fractals - Using Tensor Decompositions for Creating Self-similar Patterns}
    }

Full articles

  1. Gelß, P., Issagali, A., and Kornhuber, R. (2024). Fredholm Integral Equations for Function Approximation and the Training of Neural Networks. SIAM Journal on Mathematics of Data Science. DOI: 10.1137/23M156642X [URL] [arXiv]
    [BibTeX]
    @article{2023_GelssIssagaliKornhuber_Fredholmneuralnetworks,
      year = {2024},
      journal = {SIAM Journal on Mathematics of Data Science},
      doi = {10.1137/23M156642X},
      url = {https://epubs.siam.org/doi/abs/10.1137/23M156642X},
      archiveprefix = {arXiv},
      eprint = {2303.05262},
      primaryclass = {math.NA},
      author = {Gelß, Patrick and Issagali, Aizhan and Kornhuber, Ralf},
      title = {Fredholm Integral Equations for Function Approximation and the Training of Neural Networks}
    }
  2. Stengl, S.-M., Gelß, P., Klus, S., and Pokutta, S. (2024). Existence and Uniqueness of Solutions of the Koopman–von Neumann Equation on Bounded Domains. Journal of Physics A: Mathematical and Theoretical. DOI: 10.1088/1751-8121/ad6f7d [URL] [arXiv]
    [BibTeX]
    @article{2023_StenglGelssKlusPokutta_Koopmanvonneumann,
      year = {2024},
      journal = {Journal of Physics A: Mathematical and Theoretical},
      doi = {10.1088/1751-8121/ad6f7d},
      url = {https://iopscience.iop.org/article/10.1088/1751-8121/ad6f7d},
      archiveprefix = {arXiv},
      eprint = {2306.13504},
      primaryclass = {math.AP},
      author = {Stengl, Steven-Marian and Gelß, Patrick and Klus, Stefan and Pokutta, Sebastian},
      title = {Existence and Uniqueness of Solutions of the Koopman--von Neumann Equation on Bounded Domains}
    }
  3. Designolle, S., Iommazzo, G., Besançon, M., Knebel, S., Gelß, P., and Pokutta, S. (2023). Improved Local Models and New Bell Inequalities Via Frank-Wolfe Algorithms. Physical Review Research, 5(4). DOI: 10.1103/PhysRevResearch.5.043059 [arXiv] [slides] [code]
    [BibTeX]
    @article{2023_DesignolleEtAl_LocalmodelsBellinequalities,
      year = {2023},
      journal = {Physical Review Research},
      month = oct,
      volume = {5},
      number = {4},
      doi = {10.1103/PhysRevResearch.5.043059},
      archiveprefix = {arXiv},
      eprint = {2302.04721},
      primaryclass = {quant-ph},
      author = {Designolle, Sébastien and Iommazzo, Gabriele and Besançon, Mathieu and Knebel, Sebastian and Gelß, Patrick and Pokutta, Sebastian},
      title = {Improved Local Models and New Bell Inequalities Via Frank-Wolfe Algorithms},
      code = {https://github.com/ZIB-IOL/BellPolytopes.jl},
      slides = {https://www.pokutta.com/slides/20230808-tokyo-bell.pdf}
    }
  4. Riedel, J., Gelß, P., Klein, R., and Schmidt, B. (2023). WaveTrain: A Python Package for Numerical Quantum Mechanics of Chain-like Systems Based on Tensor Trains. The Journal of Chemical Physics, 158(16), 164801. DOI: 10.1063/5.0147314 [URL] [arXiv]
    [BibTeX]
    @article{2023_RiedelGelssKleinSchmidt_Wavetrain,
      year = {2023},
      journal = {The Journal of Chemical Physics},
      volume = {158},
      number = {16},
      pages = {164801},
      doi = {10.1063/5.0147314},
      url = {https://pubs.aip.org/aip/jcp/article/158/16/164801/2887212/WaveTrain-A-Python-package-for-numerical-quantum},
      archiveprefix = {arXiv},
      eprint = {2302.03725},
      primaryclass = {quant-ph},
      author = {Riedel, Jerome and Gelß, Patrick and Klein, Rupert and Schmidt, Burkhard},
      title = {WaveTrain: A Python Package for Numerical Quantum Mechanics of Chain-like Systems Based on Tensor Trains}
    }
  5. Gelß, P., Klein, R., Matera, S., and Schmidt, B. (2022). Solving the Time-independent Schrödinger Equation for Chains of Coupled Excitons and Phonons Using Tensor Trains. The Journal of Chemical Physics, 156, 024109. DOI: 10.1063/5.0074948 [URL] [arXiv]
    [BibTeX]
    @article{2021_GelssKleinMateraSchmidt_Tensortrainschrdinger,
      year = {2022},
      journal = {The Journal of Chemical Physics},
      volume = {156},
      pages = {024109},
      doi = {10.1063/5.0074948},
      url = {https://pubs.aip.org/aip/jcp/article/156/2/024109/2839835/Solving-the-time-independent-Schrodinger-equation},
      archiveprefix = {arXiv},
      eprint = {2109.15104},
      primaryclass = {physics.comp-ph},
      author = {Gelß, Patrick and Klein, Rupert and Matera, Sebastian and Schmidt, Burkhard},
      title = {Solving the Time-independent Schrödinger Equation for Chains of Coupled Excitons and Phonons Using Tensor Trains}
    }
  6. Nüske, F., Gelß, P., Klus, S., and Clementi, C. (2021). Tensor-based Computation of Metastable and Coherent Sets. Physica D: Nonlinear Phenomena, 427, 133018. DOI: 10.1016/j.physd.2021.133018 [URL] [arXiv]
    [BibTeX]
    @article{2019_NueskeGelssKlusClementi_Tensorkoopman,
      year = {2021},
      journal = {Physica D: Nonlinear Phenomena},
      volume = {427},
      pages = {133018},
      doi = {10.1016/j.physd.2021.133018},
      url = {https://sciencedirect.com/science/article/abs/pii/S0167278921001755},
      archiveprefix = {arXiv},
      eprint = {1908.04741},
      primaryclass = {math.NA},
      author = {Nüske, Feliks and Gelß, Patrick and Klus, Stefan and Clementi, Cecilia},
      title = {Tensor-based Computation of Metastable and Coherent Sets}
    }
  7. Gelß, P., Klus, S., Schuster, I., and Schütte, C. (2021). Feature Space Approximation for Kernel-based Supervised Learning. Knowledge-Based Systems, 221, 106935. DOI: 10.1016/j.knosys.2021.106935 [URL] [arXiv]
    [BibTeX]
    @article{2020_GelssKlusSchusterSchuette_Featureapproximation,
      year = {2021},
      journal = {Knowledge-Based Systems},
      volume = {221},
      pages = {106935},
      doi = {10.1016/j.knosys.2021.106935},
      url = {https://sciencedirect.com/science/article/abs/pii/S0950705121001982},
      archiveprefix = {arXiv},
      eprint = {2011.12651},
      primaryclass = {stat.ML},
      author = {Gelß, Patrick and Klus, Stefan and Schuster, Ingmar and Schütte, Christof},
      title = {Feature Space Approximation for Kernel-based Supervised Learning}
    }
  8. Klus, S., Gelß, P., Nüske, F., and Noé, F. (2021). Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry. Machine Learning: Science and Technology, 2(4), 18958. DOI: 10.1088/2632-2153/ac14ad [URL] [arXiv]
    [BibTeX]
    @article{2021_KlusGelssNueskeNoe_Symmetricantisymmetrickernels,
      year = {2021},
      journal = {Machine Learning: Science and Technology},
      volume = {2},
      number = {4},
      pages = {18958},
      doi = {10.1088/2632-2153/ac14ad},
      url = {https://iopscience.iop.org/article/10.1088/2632-2153/ac14ad},
      archiveprefix = {arXiv},
      eprint = {2103.17233},
      primaryclass = {quant-ph},
      author = {Klus, Stefan and Gelß, Patrick and Nüske, Feliks and Noé, Frank},
      title = {Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry}
    }
  9. Gelß, P., Klus, S., Eisert, J., and Schütte, C. (2019). Multidimensional Approximation of Nonlinear Dynamical Systems. Journal of Computational and Nonlinear Dynamics, 14(6), 25094. DOI: 10.1115/1.4043148 [URL] [arXiv]
    [BibTeX]
    @article{2018_GelssKlusEisertSchuette_Multidimensionalapproximation,
      year = {2019},
      journal = {Journal of Computational and Nonlinear Dynamics},
      volume = {14},
      number = {6},
      pages = {25094},
      doi = {10.1115/1.4043148},
      url = {https://asmedigitalcollection.asme.org/computationalnonlinear/article-abstract/14/6/061006/726935/Multidimensional-Approximation-of-Nonlinear},
      archiveprefix = {arXiv},
      eprint = {1809.02448},
      primaryclass = {math.DS},
      author = {Gelß, Patrick and Klus, Stefan and Eisert, Jens and Schütte, Christof},
      title = {Multidimensional Approximation of Nonlinear Dynamical Systems}
    }
  10. Klus, S., and Gelß, P. (2019). Tensor-based Algorithms for Image Classification. Algorithms, 12(11), 240. DOI: 10.3390/a12110240 [URL] [arXiv]
    [BibTeX]
    @article{2019_KlusGelss_Tensoralgorithmsclassification,
      year = {2019},
      journal = {Algorithms},
      volume = {12},
      number = {11},
      pages = {240},
      doi = {10.3390/a12110240},
      url = {https://mdpi.com/1999-4893/12/11/240},
      archiveprefix = {arXiv},
      eprint = {1910.02150},
      primaryclass = {cs.LG},
      author = {Klus, Stefan and Gelß, Patrick},
      title = {Tensor-based Algorithms for Image Classification}
    }
  11. Gelß, P., Klus, S., Matera, S., and Schütte, C. (2017). Nearest-neighbor Interaction Systems in the Tensor-train Format. Journal of Computational Physics, 341, 140–162. DOI: 10.1016/j.jcp.2017.04.007 [URL] [arXiv]
    [BibTeX]
    @article{2016_GelssKlusMateraSchuette_Nearestneighbortensortrain,
      year = {2017},
      journal = {Journal of Computational Physics},
      volume = {341},
      pages = {140-162},
      doi = {10.1016/j.jcp.2017.04.007},
      url = {https://sciencedirect.com/science/article/abs/pii/S0021999117302784},
      archiveprefix = {arXiv},
      eprint = {1611.03755},
      primaryclass = {math.NA},
      author = {Gelß, Patrick and Klus, Stefan and Matera, Sebastian and Schütte, Christof},
      title = {Nearest-neighbor Interaction Systems in the Tensor-train Format}
    }
  12. Klus, S., Gelß, P., Peitz, S., and Schütte, C. (2017). Tensor-based Dynamic Mode Decomposition. Nonlinearity, 31(7), 3359. DOI: 10.1088/1361-6544/aabc8f [URL] [arXiv]
    [BibTeX]
    @article{2016_KlusGelssPeitzSchuette_Tensordmd,
      year = {2017},
      journal = {Nonlinearity},
      volume = {31},
      number = {7},
      pages = {3359},
      doi = {10.1088/1361-6544/aabc8f},
      url = {https://iopscience.iop.org/article/10.1088/1361-6544/aabc8f},
      archiveprefix = {arXiv},
      eprint = {1606.06625},
      primaryclass = {math.NA},
      author = {Klus, Stefan and Gelß, Patrick and Peitz, Sebastian and Schütte, Christof},
      title = {Tensor-based Dynamic Mode Decomposition}
    }
  13. Gelß, P., Matera, S., and Schütte, C. (2016). Solving the Master Equation without Kinetic Monte Carlo - Tensor Train Approximations for a CO Oxidation Model. Journal of Computational Physics, 314, 489–502. DOI: 10.1016/j.jcp.2016.03.025 [URL]
    [BibTeX]
    @article{2016_GelssMateraSchuette_Tensortrainmasterequation,
      year = {2016},
      journal = {Journal of Computational Physics},
      volume = {314},
      pages = {489-502},
      doi = {10.1016/j.jcp.2016.03.025},
      url = {https://sciencedirect.com/science/article/abs/pii/S0021999116001777},
      author = {Gelß, Patrick and Matera, Sebastian and Schütte, Christof},
      title = {Solving the Master Equation without Kinetic Monte Carlo - Tensor Train Approximations for a CO Oxidation Model}
    }
  14. Mossner, M., Jann, J.-C., Wittig, J., Nolte, F., Fey, S., Nowak, V., Obländer, J., Pressler, J., Palme, I., Xanthopoulos, C., Boch, T., Metzgeroth, G., Röhl, H., Witt, S. H., Dukal, H., Klein, C., Schmitt, S., Gelß, P., Platzbecker, U., … Nowak, D. (2016). Mutational Hierarchies in Myelodysplastic Syndromes Dynamically Adapt and Evolve Upon Therapy Response and Failure. Blood, 128(9), 1246–1259. DOI: 10.1182/blood-2015-11-679167 [URL]
    [BibTeX]
    @article{2016_MossnerEtAl_Mutationalhierarchies,
      year = {2016},
      journal = {Blood},
      volume = {128},
      number = {9},
      pages = {1246-1259},
      doi = {10.1182/blood-2015-11-679167},
      url = {https://ashpublications.org/blood/article/128/9/1246/35782/Mutational-hierarchies-in-myelodysplastic},
      author = {Mossner, Maximilian and Jann, Johann-Christoph and Wittig, Janina and Nolte, Florian and Fey, Stephanie and Nowak, Verena and Obländer, Julia and Pressler, Jovita and Palme, Iris and Xanthopoulos, Christina and Boch, Tobias and Metzgeroth, Georgia# and Röhl, Henning and Witt, Stephanie H. and Dukal, Helene and Klein, Corinna and Schmitt, Steffen and Gelß, Patrick and Platzbecker, Uwe and Balaian, Ekaterina and Fabarius, Alice and Blum, Helmut and Schulze, Torsten J. and Meggendorfer, Manja and Haferlach, Claudia and Trumpp, Andreas and Hofmann, Wolf-Karsten and Medyouf, Hind and Nowak, Daniel},
      title = {Mutational Hierarchies in Myelodysplastic Syndromes Dynamically Adapt and Evolve Upon Therapy Response and Failure}
    }

🔬 Projects

Quantum Algorithms for Optimization

Computational devices and quantum mechanics revolutionized the 20th century. Quantum computation merges these fields to solve optimization problems faster than classical computers. This project aims to develop new quantum algorithms for general-purpose and specific applications, including optimization, mixed-integer programs, and uses in machine learning, logistics, big data, and physics. We will explore quantum dynamic programming, graph sparsification, and QAOA-type algorithms for small quantum computers.

QOPT
May 2022 to Apr 2025
2
9

💬 Talks and posters

Conference and workshop talks

Nov 2024
Quantum Machine Learning
37th SC Conference, Atlanta
Mar 2024
Tensor-based Approaches for Modeling and Simulation of Molecular Systems
94th GAMM Annual Meeting, Magdeburg
Feb 2024
Fredholm Integral Equations for the Training of Shallow Neural Networks
7th SIAM conference on uncertainty quantification (SIAM UQ)
Sep 2023
Fredholm Integral Equations for the Training of Shallow Neural Networks
7th ZIB-IMI-ISM-NUS-RIKEN-MODAL Workshop, Berlin
Sep 2023
Quantum Computing and Integer Programming
1st NHR conference
Jun 2023
Fredholm Integral Equations for the Training of Shallow Neural Networks
workshop on quantum computation and optimization, Berlin
May 2023
Quantum Machine Learning
38th International Supercomputing Conference (ISC), Hamburg
Mar 2023
Solving Kinetic Master Equations with Tensor Trains
11th SIAM CSE Conference
Sep 2022
Low-rank Tensor Decompositions of Quantum Circuits
6th ZIB-IMI-ISM-NUS-RIKEN-MODAL Workshop, Tokyo / Fukuoka
Jun 2022
Tensor-based Training of Neural Networks
24th conference of the International Linear Algebra Society (ILAS)
May 2022
Low-rank Tensor Decompositions of Quantum Circuits
3rd workshop on quantum algorithms and applications, Brussels
Dec 2019
Tensor-based Algorithms for Image Classification
Mathematics of Deep Learning
Mar 2019
The Tensor-train Format and Its Applications
89th GAMM Annual Meeting, Munich
Mar 2018
Tensor-train Approximations for Catalytic Reaction Systems
DPG Meeting of the Condensed Matter Section
Aug 2017
Solving the Master Equation without Kinetic Monte Carlo
7th International Symposium on Energy
Mar 2017
Solving the Master Equation without Kinetic Monte Carlo - Tensor Train Approximations for a CO Oxidation Model
DPG Meeting of the Condensed Matter Section
Jan 2017
SLIM-decomposition of Tensor Train Operators for Nearest-neighbor Interaction Networks
Model Reduction of Complex Dynamical Systems

Research seminar talks

Jan 2024
Tensor Decompositions
IBM QCS seminar, Zurich
Jul 2023
Fredholm Integral Equations for the Training of Shallow Neural Networks
IBM NOIP seminar, Berlin
Jun 2023
Fredholm Integral Equations for the Training of Shallow Neural Networks
DESY CQTA seminar, Zeuthen
Oct 2022
The Tensor-train Format and Its Applications
Tensor Learning Team Seminar

📅 Event Attendance

👨‍🏫 Teaching

summer 2022
Lecturer for high-dimensional discretization at FUB
winter 2021
Tutor for functional analysis at FUB
summer 2020
Tutor for dynamical systems at FUB
winter 2019
Lecturer for functional analysis at FUB
summer 2019
Lecturer for tensor decompositions and their applications at FUB
winter 2018
Tutor for functional analysis at FUB