Veröffentlichungen "Koltai, Peter"

2025

Polzin, Robert M. ; Klebanov, Ilja ; Nüsken, Nikolas ; Koltai, Peter:
Coherent Set Identification Via Direct Low Rank Maximum Likelihood Estimation.
In: Journal of Nonlinear Science. Bd. 35 (2025) . - 2.
ISSN 1432-1467
DOI: https://doi.org/10.1007/s00332-024-10091-x

2024

Chemnitz, Robin ; Engel, Maximilian ; Koltai, Peter:
Continuous-time extensions of discrete-time cocycles.
In: Proceedings of the American Mathematical Society Series B. Bd. 11 (2024) . - S. 23-35.
ISSN 2330-1511
DOI: https://doi.org/10.1090/bproc/209

Chemnitz, Robin ; Engel, Maximilian ; Koltai, Peter:
Extracting coherent sets in aperiodically driven flows from generators of Mather semigroups.
In: Discrete and Continuous Dynamical Systems. Series B. (2024) .
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2024149

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

Koltai, Peter ; Kunde, Philipp:
A Koopman-Takens theorem : Linear least squares prediction of nonlinear time series.
In: Communications in Mathematical Physics. Bd. 405 (2024) . - 120.
ISSN 1432-0916
DOI: https://doi.org/10.1007/s00220-024-05004-8

Lücke, Marvin ; Winkelmann, Stefanie ; Heitzig, Jobst ; Molkenthin, Nora ; Koltai, Peter:
Learning interpretable collective variables for spreading processes on networks.
In: Physical Review E. Bd. 109 (2024) Heft 2 . - L022301.
ISSN 2470-0053
DOI: https://doi.org/10.1103/PhysRevE.109.L022301

Froyland, Gary ; Kalia, Manu ; Koltai, Peter:
Spectral clustering of time-evolving networks using the inflated dynamic Laplacian for graphs.
arXiv , 2024
DOI: https://doi.org/10.48550/arXiv.2409.11984

2023

de Diego Unanue, Alvaro ; Froyland, Gary ; Junge, Oliver ; Koltai, Peter:
A dynamic p-Laplacian.
arXiv , 2023
DOI: https://doi.org/10.48550/arXiv.2308.05947

Froyland, Gary ; Koltai, Peter:
Detecting the birth and death of finite-time coherent sets.
In: Communications on Pure and Applied Mathematics. (2023) .
ISSN 1097-0312
DOI: https://doi.org/10.1002/cpa.22115

Lücke, Marvin ; Heitzig, Jobst ; Koltai, Peter ; Molkenthin, Nora ; Winkelmann, Stefanie:
Large population limits of Markov processes on random networks.
In: Stochastic Processes and their Applications. Bd. 166 (2023) . - 104220.
ISSN 0304-4149
DOI: https://doi.org/10.1016/j.spa.2023.09.007

Bittracher, Andreas ; Mollenhauer, Mattes ; Koltai, Peter ; Schütte, Christof:
Optimal reaction coordinates : Variational characterization and sparse computation.
In: Multiscale Modeling & Simulation. Bd. 21 (2023) Heft 2 . - S. 449-488.
ISSN 1540-3467
DOI: https://doi.org/10.1137/21M1448367

Maity, Priyanka ; Bittracher, Andreas ; Koltai, Peter ; Schumacher, Jörg:
Collective variables between large-scale states in turbulent convection.
In: Physical Review Research. Bd. 5 (2023) Heft 3 . - 033061.
ISSN 2643-1564
DOI: https://doi.org/10.1103/PhysRevResearch.5.033061

2022

Polzin, Robert ; Müller, Annette ; Rust, Henning ; Névir, Peter ; Koltai, Peter:
Direct Bayesian model reduction of smaller scale convective activity conditioned on large-scale dynamics.
In: Nonlinear Processes in Geophysics. Bd. 29 (2022) Heft 1 . - S. 37-52.
ISSN 1607-7946
DOI: https://doi.org/10.5194/npg-29-37-2022

Mollenhauer, Mattes ; Klus, Stefan ; Schütte, Christof ; Koltai, Peter:
Kernel Autocovariance Operators of Stationary Processes : Estimation and Convergence.
In: Journal of Machine Learning Research. Bd. 23 (2022) Heft 327 . - S. 1-34.
ISSN 1533-7928

Maity, Priyanka ; Koltai, Peter ; Schumacher, Jörg:
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. Bd. 380 (2022) Heft 2225 . - 20210042.
ISSN 1471-2962
DOI: https://doi.org/10.1098/rsta.2021.0042

2021

Wulkow, Niklas ; Koltai, Peter ; Sunkara, Vikram ; Schütte, Christof:
Data-driven modelling of nonlinear dynamics by barycentric coordinates and memory.
arXiv , 2021 . - 33 S.
DOI: https://doi.org/10.48550/arXiv.2112.06742

von Lindheim, Johannes ; Harikrishnan, Abhishek ; Dörffel, Tom ; Klein, Rupert ; Koltai, Peter ; Mikula, Natalia ; Müller, Annette ; Névir, Peter ; Pacey, George ; Polzin, Robert ; Vercauteren, Nikki:
Definition, detection, and tracking of persistent structures in atmospheric flows.
arXiv , 2021 . - 64 S.
DOI: https://doi.org/10.48550/arXiv.2111.13645

Bittracher, Andreas ; Klus, Stefan ; Hamzi, Boumediene ; Koltai, Peter ; Schütte, Christof:
Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds.
In: Journal of Nonlinear Science. Bd. 31 (2021) . - 3.
ISSN 1432-1467
DOI: https://doi.org/10.1007/s00332-020-09668-z

Wulkow, Niklas ; Koltai, Peter ; Schütte, Christof:
Memory-Based Reduced Modelling and Data-Based Estimation of Opinion Spreading.
In: Journal of Nonlinear Science. Bd. 31 (2021) . - 19.
ISSN 1432-1467
DOI: https://doi.org/10.1007/s00332-020-09673-2

Nüske, Feliks ; Koltai, Peter ; Boninsegna, Lorenzo ; Clementi, Cecilia:
Spectral Properties of Effective Dynamics from Conditional Expectations.
In: Entropy. Bd. 23 (2021) Heft 2 . - 134.
ISSN 1099-4300
DOI: https://doi.org/10.3390/e23020134

Helfmann, Luzie ; Heitzig, Jobst ; Koltai, Peter ; Kurths, Jürgen ; Schütte, Christof:
Statistical analysis of tipping pathways in agent-based models.
In: The European Physical Journal Special Topics. Bd. 230 (2021) . - S. 3249-3271.
ISSN 1951-6401
DOI: https://doi.org/10.1140/epjs/s11734-021-00191-0

Giulietti, Paolo ; Koltai, Peter ; Vaienti, Sandro:
Targets and holes.
In: Proceedings of the American Mathematical Society. Bd. 149 (2021) Heft 8 . - S. 3293-3306.
ISSN 1088-6826
DOI: https://doi.org/10.1090/proc/15384

Koltai, Peter ; von Lindheim, Johannes ; Neumayer, Sebastian ; Steidl, Gabriele:
Transfer operators from optimal transport plans for coherent set detection.
In: Physica D: Nonlinear Phenomena. Bd. 426 (2021) . - 132980.
ISSN 0167-2789
DOI: https://doi.org/10.1016/j.physd.2021.132980

Miron, Philippe ; Beron-Vera, Francisco J. ; Helfmann, Luzie ; Koltai, Peter:
Transition paths of marine debris and the stability of the garbage patches.
In: Chaos : An Interdisciplinary Journal of Nonlinear Science. Bd. 31 (2021) Heft 3 . - 033101.
ISSN 1089-7682
DOI: https://doi.org/10.1063/5.0030535

2020

Froyland, Gary ; Koltai, Peter ; Stahn, Martin:
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration.
In: SIAM Journal on Applied Dynamical Systems. Bd. 19 (2020) Heft 3 . - S. 1659-1700.
ISSN 1536-0040
DOI: https://doi.org/10.1137/19M1261791

Koltai, Peter ; Weiss, Stephan:
Diffusion maps embedding and transition matrix analysis of the large-scale flow structure in turbulent Rayleigh-Bénard convection.
In: Nonlinearity. Bd. 33 (2020) Heft 4 . - 1723.
ISSN 1361-6544
DOI: https://doi.org/10.1088/1361-6544/ab6a76

Banisch, Ralf ; Trstanova, Zofia ; Bittracher, Andreas ; Klus, Stefan ; Koltai, Peter:
Diffusion maps tailored to arbitrary non-degenerate Itô processes.
In: Applied and Computational Harmonic Analysis. Bd. 48 (2020) Heft 1 . - S. 242-265.
ISSN 1096-603X
DOI: https://doi.org/10.1016/j.acha.2018.05.001

Helfmann, Luzie ; Ribera Borrell, Enric ; Schütte, Christof ; Koltai, Peter:
Extending Transition Path Theory : Periodically Driven and Finite-Time Dynamics.
In: Journal of Nonlinear Science. Bd. 30 (2020) . - S. 3321-3366.
ISSN 1432-1467
DOI: https://doi.org/10.1007/s00332-020-09652-7

Mollenhauer, Mattes ; Koltai, Peter:
Nonparametric approximation of conditional expectation operators.
arXiv , 2020 . - 37 S.
DOI: https://doi.org/10.48550/arXiv.2012.12917

2019

Fackeldey, Konstantin ; Koltai, Peter ; Névir, Peter ; Rust, Henning ; Schild, Axel ; Weber, Marcus:
From metastable to coherent sets : Time-discretization schemes.
In: Chaos : An Interdisciplinary Journal of Nonlinear Science. Bd. 29 (2019) Heft 1 . - 012101.
ISSN 1089-7682
DOI: https://doi.org/10.1063/1.5058128

Koltai, Peter ; Lie, Han Cheng ; Plonka, Martin:
Fréchet differentiable drift dependence of Perron–Frobenius and Koopman operators for non-deterministic dynamics.
In: Nonlinearity. Bd. 32 (2019) Heft 11 . - S. 4232-4257.
ISSN 1361-6544
DOI: https://doi.org/10.1088/1361-6544/ab1f2a

Schneide, Christiane ; Stahn, Martin ; Pandey, Ambrish ; Junge, Oliver ; Koltai, Peter ; Padberg-Gehle, Kathrin ; Schumacher, Jörg:
Lagrangian coherent sets in turbulent Rayleigh-Bénard convection.
In: Physical Review E. Bd. 100 (2019) Heft 5 . - 053103.
ISSN 2470-0053
DOI: https://doi.org/10.1103/PhysRevE.100.053103

Miron, Philippe ; Beron-Vera, Francisco J. ; Olascoaga, Maria J. ; Koltai, Peter:
Markov-chain-inspired search for MH370.
In: Chaos : An Interdisciplinary Journal of Nonlinear Science. Bd. 29 (2019) Heft 4 . - 041105.
ISSN 1089-7682
DOI: https://doi.org/10.1063/1.5092132

Banisch, Ralf ; Koltai, Peter ; Padberg-Gehle, Kathrin:
Network measures of mixing.
In: Chaos : An Interdisciplinary Journal of Nonlinear Science. Bd. 29 (2019) Heft 6 . - 063125.
ISSN 1089-7682
DOI: https://doi.org/10.1063/1.5087632

Gerlach, Raphael ; Koltai, Peter ; Dellnitz, Michael:
Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems.
arXiv , 2019 . - 22 S.
DOI: https://doi.org/10.48550/arXiv.1902.08824

2018

Klus, Stefan ; Nüske, Feliks ; Koltai, Peter ; Wu, Hao ; Kevrekidis, Ioannis ; Schütte, Christof ; Noé, Frank:
Data-driven model reduction and transfer operator approximation.
In: Journal of Nonlinear Science. Bd. 28 (2018) Heft 3 . - S. 985-1010.
ISSN 1432-1467
DOI: https://doi.org/10.1007/s00332-017-9437-7

Koltai, Peter ; Renger, D. R. Michiel:
From Large Deviations to Semidistances of Transport and Mixing : Coherence Analysis for Finite Lagrangian Data.
In: Journal of Nonlinear Science. Bd. 28 (2018) . - S. 1915-1957.
ISSN 1432-1467
DOI: https://doi.org/10.1007/s00332-018-9471-0

Koltai, Peter ; Schütte, Christof:
A Multiscale Perturbation Expansion Approach for Markov State Modeling of Nonstationary Molecular Dynamics.
In: Multiscale Modeling & Simulation. Bd. 16 (2018) Heft 4 . - S. 1455-1485.
ISSN 1540-3467
DOI: https://doi.org/10.1137/17M1146403

Koltai, Peter ; Wu, Hao ; Noé, Frank ; Schütte, Christof:
Optimal Data-Driven Estimation of Generalized Markov State Models for Non-Equilibrium Dynamics.
In: Computation. Bd. 6 (2018) Heft 1 . - 22.
ISSN 2079-3197
DOI: https://doi.org/10.3390/computation6010022

Bittracher, Andreas ; Koltai, Peter ; Klus, Stefan ; Banisch, Ralf ; Dellnitz, Michael ; Schütte, Christof:
Transition Manifolds of Complex Metastable Systems.
In: Journal of Nonlinear Science. Bd. 28 (2018) . - S. 471-512.
ISSN 1432-1467
DOI: https://doi.org/10.1007/s00332-017-9415-0

2017

Froyland, Gary ; Koltai, Peter:
Estimating long-term behavior of periodically driven flows without trajectory integration.
In: Nonlinearity. Bd. 30 (2017) Heft 5 . - S. 1948-1986.
ISSN 1361-6544
DOI: https://doi.org/10.1088/1361-6544/aa6693

Banisch, Ralf ; Koltai, Peter:
Understanding the geometry of transport : Diffusion maps for Lagrangian trajectory data unravel coherent sets.
In: Chaos : An Interdisciplinary Journal of Nonlinear Science. Bd. 27 (2017) Heft 3 . - 035804.
ISSN 1089-7682
DOI: https://doi.org/10.1063/1.4971788

Wu, Hao ; Nüske, Feliks ; Paul, Fabian ; Klus, Stefan ; Koltai, Peter ; Noé, Frank:
Variational Koopman models : Slow collective variables and molecular kinetics from short off-equilibrium simulations.
In: The Journal of Chemical Physics. Bd. 146 (2017) Heft 15 . - 154104.
ISSN 0021-9606
DOI: https://doi.org/10.1063/1.4979344

2016

Koltai, Peter ; Ciccotti, Giovanni ; Schütte, Christof:
On metastability and Markov state models for non-stationary molecular dynamics.
In: The Journal of Chemical Physics. Bd. 145 (2016) Heft 17 . - 174103.
ISSN 0021-9606
DOI: https://doi.org/10.1063/1.4966157

Klus, Stefan ; Koltai, Peter ; Schütte, Christof:
On the numerical approximation of the Perron-Frobenius and Koopman operator.
In: Journal of Computational Dynamics. Bd. 3 (2016) Heft 1 . - S. 51-79.
ISSN 2158-2491
DOI: https://doi.org/10.3934/jcd.2016003

2015

Bittracher, Andreas ; Hartmann, Carsten ; Junge, Oliver ; Koltai, Peter:
Pseudo generators for under-resolved molecular dynamics.
In: The European Physical Journal Special Topics. Bd. 224 (2015) Heft 12 . - S. 2463-2490.
ISSN 1951-6401
DOI: https://doi.org/10.1140/epjst/e2015-02422-y

Bittracher, Andreas ; Koltai, Peter ; Junge, Oliver:
Pseudogenerators of Spatial Transfer Operators.
In: SIAM Journal on Applied Dynamical Systems. Bd. 14 (2015) Heft 3 . - S. 1478-1517.
ISSN 1536-0040
DOI: https://doi.org/10.1137/14099872X

2014

Grüne, Lars ; Hirche, Sandra ; Junge, Oliver ; Koltai, Peter ; Lehmann, Daniel ; Lunze, Jan ; Molin, Adam ; Sailer, Rudolf ; Sigurani, Manuela ; Stöcker, Christian ; Wirth, Fabian:
Event-based control.
In: Lunze, Jan (ed.): Control theory of digitally networked dynamic systems. - Cham : Springer , 2014 . - S. 169-261
ISBN 978-3-319-01130-1
DOI: https://doi.org/10.1007/978-3-319-01131-8_5

Koltai, Peter ; Junge, Oliver:
Optimal value functions for weakly coupled systems : a posteriori estimates.
In: ZAMM : Journal of Applied Mathematics and Mechanics = Zeitschrift für angewandte Mathematik und Mechanik. Bd. 94 (2014) Heft 4 . - S. 345-355.
ISSN 1521-4001
DOI: https://doi.org/10.1002/zamm.201100138

Koltai, Peter ; Volf, Alexander:
Optimizing the stable behavior of parameter-dependent dynamical systems : maximal domains of attraction, minimal absorption times.
In: Journal of Computational Dynamics. Bd. 1 (2014) Heft 2 . - S. 339-356.
ISSN 2158-2491
DOI: https://doi.org/10.3934/jcd.2014.1.339

Koltai, Peter ; Junge, Oliver:
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
ISBN 978-90-367-6321-9

Koltai, Peter:
Split optimal policy iteration for LQR problems.
arXiv , 2014 . - 14 S.
DOI: https://doi.org/10.48550/arXiv.1404.5209

2013

Froyland, Gary ; Junge, Oliver ; Koltai, Peter:
Estimating long term behavior of flows without trajectory integration : the infinitesimal generator approach.
In: SIAM Journal on Numerical Analysis. Bd. 51 (2013) Heft 1 . - S. 223-247.
ISSN 1095-7170
DOI: https://doi.org/10.1137/110819986

2011

Koltai, Peter:
Discrete infinitesimal generator of the Frobenius-Perron operator semigroup associated with "outflow systems".
arXiv , 2011 . - 4 S.
DOI: https://doi.org/10.48550/arXiv.1103.0530

Koltai, Peter:
Efficient approximation methods for the global long-term behavior of dynamical systems : Theory, algorithms and examples.
Berlin : Logos-Verlag , 2011 . - VIII, 162 S.
ISBN 978-3-8325-2752-5

Koltai, Peter:
A stochastic approach for computing the domain of attraction without trajectory simulation.
In: Conference Publications / American Institute of Mathematical Sciences. (2011) . - S. 854-863.
DOI: https://doi.org/10.3934/proc.2011.2011.854

2009

Junge, Oliver ; Koltai, Peter:
Discretization of the Frobenius-Perron Operator Using a Sparse Haar Tensor Basis : The Sparse Ulam Method.
In: SIAM Journal on Numerical Analysis. Bd. 47 (2009) Heft 5 . - S. 3464-3485.
ISSN 1095-7170
DOI: https://doi.org/10.1137/080716864

Friesecke, Gero ; Junge, Oliver ; Koltai, Peter:
Mean Field Approximation in Conformation Dynamics.
In: Multiscale Modeling & Simulation. Bd. 8 (2009) Heft 1 . - S. 254-268.
ISSN 1540-3467
DOI: https://doi.org/10.1137/080745262