267 citations · 1.1k across the 40 of their papers we have counts for
25 papers · 1 filter
A dynamic -Laplacian
Alvaro de Diego Unanue, Gary Froyland, Oliver Junge +1
We generalise the dynamic Laplacian introduced in (Froyland, 2015) to a dynamic -Laplacian, in analogy to the generalisation of the standard -Laplacian to the standard -La…
A Koopman-Takens theorem: Linear least squares prediction of nonlinear time series
Péter Koltai, Philipp Kunde
The least squares linear filter, also called the Wiener filter, is a popular tool to predict the next element(s) of time series by linear combination of time-delayed observations.…
Continuous-time extensions of discrete-time cocycles
Robin Chemnitz, Maximilian Engel, Péter Koltai
We consider linear cocycles taking values in driven by homeomorphic transformations of a smooth manifold, in discrete and continuous time. We show that…
Data-driven modelling of nonlinear dynamics by barycentric coordinates and memory
Niklas Wulkow, Péter Koltai, Vikram Sunkara +1
We present a numerical method to model dynamical systems from data. We use the recently introduced method Scalable Probabilistic Approximation (SPA) to project points from a Euclid…
Optimal Reaction Coordinates: Variational Characterization and Sparse Computation
Andreas Bittracher, Mattes Mollenhauer, Péter Koltai +1
Reaction Coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and…
Detecting the birth and death of finite-time coherent sets
Gary Froyland, Péter Koltai
Finite-time coherent sets (FTCSs) are distinguished regions of phase space that resist mixing with the surrounding space for some finite period of time; physical manifestations inc…
Memory-based reduced modelling and data-based estimation of opinion spreading
Niklas Wulkow, Péter Koltai, Christof Schütte
We investigate opinion dynamics based on an agent-based model, and are interested in predicting the evolution of the percentages of the entire agent population that share an opinio…
Extending Transition Path Theory: Periodically-Driven and Finite-Time Dynamics
Luzie Helfmann, Enric Ribera Borrell, Christof Schütte +1
Given two distinct subsets in the state space of some dynamical system, Transition Path Theory (TPT) was successfully used to describe the statistical behavior of transitions…
Targets and Holes
P. Giulietti, P. Koltai, S. Vaienti
We address the extreme value problem of a one-dimensional dynamical system approaching a fixed target while constrained to avoid a fixed set which can be thought of as a small hole…
Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds
Andreas Bittracher, Stefan Klus, Boumediene Hamzi +2
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems.…
Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems
Raphael Gerlach, Péter Koltai, Michael Dellnitz
Embedding techniques allow the approximations of finite dimensional attractors and manifolds of infinite dimensional dynamical systems via subdivision and continuation methods. The…
Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration
Gary Froyland, Péter Koltai, Martin Stahn
Understanding the macroscopic behavior of dynamical systems is an important tool to unravel transport mechanisms in complex flows. A decomposition of the state space into coherent…
Spectral Properties of Effective Dynamics from Conditional Expectations
Feliks Nüske, Péter Koltai, Lorenzo Boninsegna +1
The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffu…
Network Measures of Mixing
Ralf Banisch, Péter Koltai, Kathrin Padberg-Gehle
Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this cont…
Optimal data-driven estimation of generalized Markov state models for non-equilibrium dynamics
Péter Koltai, Hao Wu, Frank Noé +1
There are multiple ways in which a stochastic system can be out of statistical equilibrium. It might be subject to time-varying forcing; or be in a transient phase on its way towar…
Diffusion maps tailored to arbitrary non-degenerate Ito processes
Ralf Banisch, Zofia Trstanova, Andreas Bittracher +2
We present two generalizations of the popular diffusion maps algorithm. The first generalization replaces the drift term in diffusion maps, which is the gradient of the sampling de…
From large deviations to semidistances of transport and mixing: coherence analysis for finite Lagrangian data
Péter Koltai, D. R. Michiel Renger
One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, fini…
Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics
Andreas Bittracher, Péter Koltai, Stefan Klus +3
We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhi…
Data-driven model reduction and transfer operator approximation
Stefan Klus, Feliks Nüske, Péter Koltai +4
In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to ap…
Understanding the geometry of transport: diffusion maps for Lagrangian trajectory data unravel coherent sets
Ralf Banisch, Péter Koltai
Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an im…
On the numerical approximation of the Perron-Frobenius and Koopman operator
Stefan Klus, Péter Koltai, Christof Schütte
Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynami…
Estimating long-term behavior of periodically driven flows without trajectory integration
Gary Froyland, Péter Koltai
Periodically driven flows are fundamental models of chaotic behavior and the study of their transport properties is an active area of research. A well-known analytic construction i…
Pseudo generators for under-resolved molecular dynamics
Andreas Bittracher, Carsten Hartmann, Oliver Junge +1
Many features of a molecule which are of physical interest (e.g. molecular conformations, reaction rates) are described in terms of its dynamics in configuration space. This articl…
Pseudo generators of spatial transfer operators
Andreas Bittracher, Péter Koltai, Oliver Junge
Metastable behavior in dynamical systems may be a significant challenge for a simulation based analysis. In recent years, transfer operator based approaches to problems exhibiting…