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.

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Preprints

1. 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. [arXiv]
   [BibTeX]

   @misc{dibkgp_bell_23,
     archiveprefix = {arXiv},
     eprint = {2302.04721},
     primaryclass = {quant-ph},
     year = {2023},
     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}
   }

2. Gelß, P., Issagali, A., and Kornhuber, R. (2023). Fredholm Integral Equations for Function Approximation and the Training of Neural Networks. [arXiv]
   [BibTeX]

   @misc{gik_fredholm_23,
     archiveprefix = {arXiv},
     eprint = {2303.05262},
     primaryclass = {math.NA},
     year = {2023},
     author = {Gelß, Patrick and Issagali, Aizhan and Kornhuber, Ralf},
     title = {Fredholm Integral Equations for Function Approximation and the Training of Neural Networks}
   }

3. 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{gkms_tdse_23,
     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}
   }

4. Gelß, P., Klus, S., Shakibaei, Z., and Pokutta, S. (2022). Low-rank Tensor Decompositions of Quantum Circuits. [arXiv]
   [BibTeX]

   @misc{gksp_lowrankqc_22,
     archiveprefix = {arXiv},
     eprint = {2205.09882},
     primaryclass = {quant-ph},
     year = {2022},
     author = {Gelß, Patrick and Klus, Stefan and Shakibaei, Zarin and Pokutta, Sebastian},
     title = {Low-rank Tensor Decompositions of Quantum Circuits}
   }

5. Gelß, P., and Schütte, C. (2018). Tensor-generated Fractals - Using Tensor Decompositions for Creating Self-similar Patterns. [arXiv]
   [BibTeX]

   @misc{gs_fractals_18,
     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. 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{rgks_wavetrain_23,
     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}
   }

2. 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{gkms_tise_22,
     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}
   }

3. 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{gkss_fsa_21,
     year = {2021},
     journal = {Knowledge-Based Systems},
     volume = {221},
     pages = {106935},
     doi = {10.1016/j.knosys.2021.106935},
     url = {https://www.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}
   }

4. 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{kgnn_antisymmetric_21,
     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}
   }

5. 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{ngkc_metastable_2021,
     year = {2021},
     journal = {Physica D: Nonlinear Phenomena},
     volume = {427},
     pages = {133018},
     doi = {10.1016/j.physd.2021.133018},
     url = {https://www.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}
   }

6. 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{gkes_mandy_19,
     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}
   }

7. Klus, S., and Gelß, P. (2019). Tensor-based Algorithms for Image Classification. Algorithms, 12(11), 240. DOI: 10.3390/a12110240 [URL] [arXiv]
   [BibTeX]

   @article{kg_imageclass_19,
     year = {2019},
     journal = {Algorithms},
     volume = {12},
     number = {11},
     pages = {240},
     doi = {10.3390/a12110240},
     url = {https://www.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}
   }

8. 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{gkms_slim_17,
     year = {2017},
     journal = {Journal of Computational Physics},
     volume = {341},
     pages = {140-162},
     doi = {10.1016/j.jcp.2017.04.007},
     url = {https://www.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}
   }

9. 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{kgps_dmd_17,
     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}
   }

10. 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{gms_oxidation_16,
      year = {2016},
      journal = {Journal of Computational Physics},
      volume = {314},
      pages = {489-502},
      doi = {10.1016/j.jcp.2016.03.025},
      url = {https://www.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}
    }

11. 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{mjgmn_mutational_16,
      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}
    }

Conference and workshop talks

Research seminar talks