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Faculty of mathematics, physics & computer science

Dynamical Systems and Data – Prof. Dr Péter Koltai

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Prof. Dr Péter Koltai

Faculty of mathematics, physics & computer science

Head of Chair

Faculty of mathematics, physics & computer science

  • dynamical systems, stochastic processes, ergodic theory and their applications
  • processes on and of networks: graph theory and model reduction
  • time series: operator-theoretic analysis, spectral theory
  • data science and machine learning: data-driven modeling

Faculty of mathematics, physics & computer science



Robin Chemnitz, Maximilian Engel, Peter Koltai: Continuous-time extensions of discrete-time cocycles. In: Proceedings of the American Mathematical Society Series B, 11 (2024). - S. 23-35.

Robin Chemnitz, Maximilian Engel, Peter Koltai: Extracting coherent sets in aperiodically driven flows from generators of Mather semigroups.. - arXiv, 2024. -

Jason Atnip, Gary Froyland, Peter Koltai: An inflated dynamic Laplacian to track the emergence and disappearance of semi-material coherent sets.. - arXiv, 2024. -

Peter Koltai, Philipp Kunde: A Koopman-Takens theorem : Linear least squares prediction of nonlinear time series. In: Communications in Mathematical Physics, 405 (2024). - .

Marvin Lücke, Stefanie Winkelmann, Jobst Heitzig, Nora Molkenthin, Peter Koltai: Learning interpretable collective variables for spreading processes on networks. In: Physical Review E, 109 (2024). - .


Robert Polzin, Ilja Klebanov, Nikolas Nüsken, Peter Koltai: Nonnegative matrix factorization for coherent set identification by direct low rank maximum likelihood estimation.. - arXiv, 2023-08-15. -

Alvaro de Diego Unanue, Gary Froyland, Oliver Junge, Peter Koltai: A dynamic p-Laplacian.. - arXiv, 2023-08-11. -

Priyanka Maity, Andreas Bittracher, Peter Koltai, Jörg Schumacher: Collective variables between large-scale states in turbulent convection. In: Physical Review Research, 5 (2023). - .

Gary Froyland, Peter Koltai: Detecting the birth and death of finite-time coherent sets. In: Communications on Pure and Applied Mathematics, (2023). - .

Marvin Lücke, Jobst Heitzig, Peter Koltai, Nora Molkenthin, Stefanie Winkelmann: Large population limits of Markov processes on random networks. In: Stochastic Processes and their Applications, 166 (2023). - .

Andreas Bittracher, Mattes Mollenhauer, Peter Koltai, Christof Schütte: Optimal reaction coordinates : Variational characterization and sparse computation. In: Multiscale Modeling & Simulation, 21 (2023). - S. 449-488.


Robert Polzin, Annette Müller, Henning Rust, Peter Névir, Peter Koltai: Direct Bayesian model reduction of smaller scale convective activity conditioned on large-scale dynamics. In: Nonlinear Processes in Geophysics, 29 (2022). - S. 37-52.

Mattes Mollenhauer, Stefan Klus, Christof Schütte, Peter Koltai: Kernel Autocovariance Operators of Stationary Processes : Estimation and Convergence. In: Journal of Machine Learning Research, 23 (2022). - S. 1-34.

Priyanka Maity, Peter Koltai, Jörg Schumacher: Large-scale flow in a cubic Rayleigh-Bénard cell : long-term turbulence statistics and Markovianity of macrostate transitions. In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380 (2022). - .


Niklas Wulkow, Peter Koltai, Vikram Sunkara, Christof Schütte: Data-driven modelling of nonlinear dynamics by barycentric coordinates and memory.. - arXiv, 2021. - 33 S.

Johannes von Lindheim, Abhishek Harikrishnan, Tom Dörffel, Rupert Klein, Peter Koltai, Natalia Mikula, Annette Müller, Peter Névir, George Pacey, Robert Polzin, Nikki Vercauteren: Definition, detection, and tracking of persistent structures in atmospheric flows.. - arXiv, 2021. - 64 S.

Andreas Bittracher, Stefan Klus, Boumediene Hamzi, Peter Koltai, Christof Schütte: Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds. In: Journal of Nonlinear Science, 31 (2021). - .

Niklas Wulkow, Peter Koltai, Christof Schütte: Memory-Based Reduced Modelling and Data-Based Estimation of Opinion Spreading. In: Journal of Nonlinear Science, 31 (2021). - .

Feliks Nüske, Peter Koltai, Lorenzo Boninsegna, Cecilia Clementi: Spectral Properties of Effective Dynamics from Conditional Expectations. In: Entropy, 23 (2021). - .

Luzie Helfmann, Jobst Heitzig, Peter Koltai, Jürgen Kurths, Christof Schütte: Statistical analysis of tipping pathways in agent-based models. In: The European Physical Journal Special Topics, 230 (2021). - S. 3249-3271.

Paolo Giulietti, Peter Koltai, Sandro Vaienti: Targets and holes. In: Proceedings of the American Mathematical Society, 149 (2021). - S. 3293-3306.

Peter Koltai, Johannes von Lindheim, Sebastian Neumayer, Gabriele Steidl: Transfer operators from optimal transport plans for coherent set detection. In: Physica D: Nonlinear Phenomena, 426 (2021). - .

Philippe Miron, Francisco J. Beron-Vera, Luzie Helfmann, Peter Koltai: Transition paths of marine debris and the stability of the garbage patches. In: Chaos : An Interdisciplinary Journal of Nonlinear Science, 31 (2021). - .


Gary Froyland, Peter Koltai, Martin Stahn: Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration. In: SIAM Journal on Applied Dynamical Systems, 19 (2020). - S. 1659-1700.

Peter Koltai, Stephan Weiss: Diffusion maps embedding and transition matrix analysis of the large-scale flow structure in turbulent Rayleigh-Bénard convection. In: Nonlinearity, 33 (2020). - .

Ralf Banisch, Zofia Trstanova, Andreas Bittracher, Stefan Klus, Peter Koltai: Diffusion maps tailored to arbitrary non-degenerate Itô processes. In: Applied and Computational Harmonic Analysis, 48 (2020). - S. 242-265.

Luzie Helfmann, Enric Ribera Borrell, Christof Schütte, Peter Koltai: Extending Transition Path Theory : Periodically Driven and Finite-Time Dynamics. In: Journal of Nonlinear Science, 30 (2020). - S. 3321-3366.

Mattes Mollenhauer, Peter Koltai: Nonparametric approximation of conditional expectation operators.. - arXiv, 2020. - 37 S.


Konstantin Fackeldey, Peter Koltai, Peter Névir, Henning Rust, Axel Schild, Marcus Weber: From metastable to coherent sets : Time-discretization schemes. In: Chaos : An Interdisciplinary Journal of Nonlinear Science, 29 (2019). - .

Peter Koltai, Han Cheng Lie, Martin Plonka: Fréchet differentiable drift dependence of Perron–Frobenius and Koopman operators for non-deterministic dynamics. In: Nonlinearity, 32 (2019). - S. 4232-4257.

Christiane Schneide, Martin Stahn, Ambrish Pandey, Oliver Junge, Peter Koltai, Kathrin Padberg-Gehle, Jörg Schumacher: Lagrangian coherent sets in turbulent Rayleigh-Bénard convection. In: Physical Review E, 100 (2019). - .

Philippe Miron, Francisco J. Beron-Vera, Maria J. Olascoaga, Peter Koltai: Markov-chain-inspired search for MH370. In: Chaos : An Interdisciplinary Journal of Nonlinear Science, 29 (2019). - .

Ralf Banisch, Peter Koltai, Kathrin Padberg-Gehle: Network measures of mixing. In: Chaos : An Interdisciplinary Journal of Nonlinear Science, 29 (2019). - .

Raphael Gerlach, Peter Koltai, Michael Dellnitz: Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems.. - arXiv, 2019. - 22 S.


Stefan Klus, Feliks Nüske, Peter Koltai, Hao Wu, Ioannis Kevrekidis, Christof Schütte, Frank Noé: Data-driven model reduction and transfer operator approximation. In: Journal of Nonlinear Science, 28 (2018). - S. 985-1010.

Peter Koltai, D. R. Michiel Renger: From Large Deviations to Semidistances of Transport and Mixing : Coherence Analysis for Finite Lagrangian Data. In: Journal of Nonlinear Science, 28 (2018). - S. 1915-1957.

Peter Koltai, Christof Schütte: A Multiscale Perturbation Expansion Approach for Markov State Modeling of Nonstationary Molecular Dynamics. In: Multiscale Modeling & Simulation, 16 (2018). - S. 1455-1485.

Peter Koltai, Hao Wu, Frank Noé, Christof Schütte: Optimal Data-Driven Estimation of Generalized Markov State Models for Non-Equilibrium Dynamics. In: Computation, 6 (2018). - .

Andreas Bittracher, Peter Koltai, Stefan Klus, Ralf Banisch, Michael Dellnitz, Christof Schütte: Transition Manifolds of Complex Metastable Systems. In: Journal of Nonlinear Science, 28 (2018). - S. 471-512.


Gary Froyland, Peter Koltai: Estimating long-term behavior of periodically driven flows without trajectory integration. In: Nonlinearity, 30 (2017). - S. 1948-1986.

Ralf Banisch, Peter Koltai: Understanding the geometry of transport : Diffusion maps for Lagrangian trajectory data unravel coherent sets. In: Chaos : An Interdisciplinary Journal of Nonlinear Science, 27 (2017). - .

Hao Wu, Feliks Nüske, Fabian Paul, Stefan Klus, Peter Koltai, Frank Noé: Variational Koopman models : Slow collective variables and molecular kinetics from short off-equilibrium simulations. In: The Journal of Chemical Physics, 146 (2017). - .


Peter Koltai, Giovanni Ciccotti, Christof Schütte: On metastability and Markov state models for non-stationary molecular dynamics. In: The Journal of Chemical Physics, 145 (2016). - .

Stefan Klus, Peter Koltai, Christof Schütte: On the numerical approximation of the Perron-Frobenius and Koopman operator. In: Journal of Computational Dynamics, 3 (2016). - S. 51-79.


Andreas Bittracher, Carsten Hartmann, Oliver Junge, Peter Koltai: Pseudo generators for under-resolved molecular dynamics. In: The European Physical Journal Special Topics, 224 (2015). - S. 2463-2490.

Andreas Bittracher, Peter Koltai, Oliver Junge: Pseudogenerators of Spatial Transfer Operators. In: SIAM Journal on Applied Dynamical Systems, 14 (2015). - S. 1478-1517.


Lars Grüne, Sandra Hirche, Oliver Junge, Peter Koltai, Daniel Lehmann, Jan Lunze, Adam Molin, Rudolf Sailer, Manuela Sigurani, Christian Stöcker, Fabian Wirth: Event-based control. In: Lunze, Jan (ed.): Control theory of digitally networked dynamic systems. - Cham : Springer, 2014. - S. 169-261.

Peter Koltai, Oliver Junge: Optimal value functions for weakly coupled systems : a posteriori estimates. In: ZAMM : Journal of Applied Mathematics and Mechanics = Zeitschrift für angewandte Mathematik und Mechanik, 94 (2014). - S. 345-355.

Peter Koltai, Alexander Volf: Optimizing the stable behavior of parameter-dependent dynamical systems : maximal domains of attraction, minimal absorption times. In: Journal of Computational Dynamics, 1 (2014). - S. 339-356.

Peter Koltai, Oliver Junge: Quantized nonlinear feedback design by a split dynamic programming approach. In: MTNS 2014 : the 21st International Symposium on Mathematical Theory of Networks and Systems ; Proceedings. - Groningen, The Netherlands : University of Groningen, 2014.

Peter Koltai: Split optimal policy iteration for LQR problems.. - arXiv, 2014. - 14 S.


Gary Froyland, Oliver Junge, Peter Koltai: Estimating long term behavior of flows without trajectory integration : the infinitesimal generator approach. In: SIAM Journal on Numerical Analysis, 51 (2013). - S. 223-247.


Peter Koltai: Discrete infinitesimal generator of the Frobenius-Perron operator semigroup associated with "outflow systems".. - arXiv, 2011. - 4 S.

Peter Koltai: Efficient approximation methods for the global long-term behavior of dynamical systems : Theory, algorithms and examples. - Berlin : Logos-Verlag, 2011. - VIII, 162 S.

Peter Koltai: A stochastic approach for computing the domain of attraction without trajectory simulation. In: Conference Publications / American Institute of Mathematical Sciences, (2011). - S. 854-863.


Oliver Junge, Peter Koltai: Discretization of the Frobenius-Perron Operator Using a Sparse Haar Tensor Basis : The Sparse Ulam Method. In: SIAM Journal on Numerical Analysis, 47 (2009). - S. 3464-3485.

Gero Friesecke, Oliver Junge, Peter Koltai: Mean Field Approximation in Conformation Dynamics. In: Multiscale Modeling & Simulation, 8 (2009). - S. 254-268.

Faculty of mathematics, physics & computer science

Prof. Dr Péter Koltai
Head of Chair

Zapf 1 - Nürnberger Str. 38

Room: 1.2.11

Phone: +49 (0)921 55-4547
E-mail: Peter.Koltai@uni-bayreuth.de

Webmaster: Prof. Dr. Péter Koltai

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