@article{GelssKlusEisertetal.2019, author = {Gelß, Patrick and Klus, Stefan and Eisert, Jens and Sch{\"u}tte, Christof}, title = {Multidimensional Approximation of Nonlinear Dynamical Systems}, volume = {14}, journal = {Journal of Computational and Nonlinear Dynamics}, number = {6}, doi = {10.1115/1.4043148}, year = {2019}, abstract = {A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models. In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities. However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality. To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions. The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems.}, language = {en} } @article{KlusGelssPeitzetal.2018, author = {Klus, Stefan and Gelß, Patrick and Peitz, Sebastian and Sch{\"u}tte, Christof}, title = {Tensor-based dynamic mode decomposition}, volume = {31}, journal = {Nonlinearity}, number = {7}, publisher = {IOP Publishing Ltd \& London Mathematical Society}, doi = {10.1088/1361-6544/aabc8f}, year = {2018}, language = {en} } @article{KlusGelss2025, author = {Klus, Stefan and Gelß, Patrick}, title = {Continuous optimization methods for the graph isomorphism problem}, volume = {14}, journal = {Information and Inference: A Journal of the IMA}, number = {2}, doi = {10.1093/imaiai/iaaf011}, year = {2025}, language = {en} } @article{StenglGelssKlusetal.2024, 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}, volume = {57}, journal = {Journal of Physics A: Mathematical and Theoretical}, number = {39}, doi = {10.1088/1751-8121/ad6f7d}, year = {2024}, language = {en} } @article{GelssKlusKnebeletal.2022, author = {Gelß, Patrick and Klus, Stefan and Knebel, Sebastian and Shakibaei, Zarin and Pokutta, Sebastian}, title = {Low-Rank Tensor Decompositions of Quantum Circuits}, journal = {Journal of Computational Physics}, arxiv = {http://arxiv.org/abs/2205.09882}, year = {2022}, abstract = {Quantum computing is arguably one of the most revolutionary and disruptive technologies of this century. Due to the ever-increasing number of potential applications as well as the continuing rise in complexity, the development, simulation, optimization, and physical realization of quantum circuits is of utmost importance for designing novel algorithms. We show how matrix product states (MPSs) and matrix product operators (MPOs) can be used to express certain quantum states, quantum gates, and entire quantum circuits as low-rank tensors. This enables the analysis and simulation of complex quantum circuits on classical computers and to gain insight into the underlying structure of the system. We present different examples to demonstrate the advantages of MPO formulations and show that they are more efficient than conventional techniques if the bond dimensions of the wave function representation can be kept small throughout the simulation.}, language = {en} }