List of Publications

S. Designolle, G. Iommazzo, M. Besancon, S. Knebel, P. Gelß, S. Pokutta. Improved local models and new Bell inequalities via Frank-Wolfe algorithms. Physical Review Research 5, 043059. DOI: 10.1103/PhysRevResearch.5.043059. arXiv: 2302.04721

S.-M. Stengl, P. Gelß, S. Klus, and S. Pokutta. Existence and Uniqueness of Solutions of the Koopman–von Neumann Equation on Bounded Domains. submitted. arXiv: 2306.13504

P. Gelß, A. Issagali, and R. Kornhuber. Fredholm integral equations for function approximation and the training of neural networks. submitted. arXiv: 2303.05262

J. Riedel, P. Gelß, R. Klein, and B. Schmidt. WaveTrain: A Python Package for Numerical Quantum Mechanics of Chain-Like Systems Based on Tensor Trains. Journal of Chemical Physics 158 (16). DOI: 10.1063/5.0147314, arXiv: 2302.03725

P. Gelß, R. Klein, S. Matera, and B. Schmidt. Quantum dynamics of coupled excitons and phonons in chain-like systems: tensor train approaches and higher-order propagators. submitted. arXiv: 2302.03568

P. Gelß, S. Klus, S. Knebel, Z. Shakibaei, and S. Pokutta. Low-Rank Tensor Decompositions of Quantum Circuits. submitted. arXiv: 2205.09882

P. Gelß, R. Klein, S. Matera, and B. Schmidt. 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, arXiv: 2109.15104

F. Nüske, P. Gelß, S. Klus, and C. Clementi. Tensor-Based Computation of Metastable and Coherent Sets. Physica D 427, 133018. DOI: 10.1016/j.physd.2021.133018, arXiv: 1908.04741

S. Klus, P. Gelß, F. Nüske, and F. Noé. Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry. Machine Learning: Science and Technology 2 (4), 045016. DOI: 10.1088/2632-2153/ac14ad, arXiv: 2103.17233

P. Gelß, S. Klus, I. Schuster, and C. Schütte. Feature Space Approximation for Kernel-Based Supervised Learning. Knowledge-Based Systems 221, 106935. DOI: 10.1016/j.knosys.2021.106935, arXiv: 2011.12651

S. Klus and P. Gelß. Tensor-Based Algorithms for Image Classification. Algorithms 12 (11), 240. DOI: 10.3390/a12110240 , arXiv: 1910.02150

P. Gelß, S. Klus, J. Eisert, and C. Schütte. Multidimensional Approximation of Nonlinear Dynamical Systems. Journal of Computational and Nonlinear Dynamics 14, 061006. DOI: 10.1115/1.4043148 , arXiv:  1809.02448

P. Gelß and C. Schütte. Tensor-Generated Fractals: Using Tensor Decompositions for Creating Self-Similar Patterns. arXiv:  1812.00814

P. Gelß. The Tensor-Train Format and Its Applications – Modeling and Analysis of Chemical Reaction Networks, Catalytic Processes, Fluid Flows, and Brownian Dynamics. Dissertation, Freie Universität Berlin.  FUB Refubium

P. Gelß, S. Klus, S. Matera, and C. Schütte. Nearest-Neighbor Interaction Systems in the Tensor-Train Format. Journal of Computational Physics 341, pp. 140-162, DOI: 10.1016/j.jcp.2017.04.007 , arXiv: 1611.03755

S. Klus, P. Gelß, S. Peitz, and C. Schütte. Tensor-Based Dynamic Mode Decomposition. Nonlinearity 31, 3359. DOI: 10.1088/1361-6544/aabc8f, arXiv: 1606.06625

P. Gelß, S. Matera, and C. Schütte. Solving the Master Equation without Kinetic Monte Carlo: Tensor Train Approximations for a CO Oxidation Model. Journal of Computational Physics 314, pp. 489-502. DOI:  10.1016/j.jcp.2016.03.025