58 citations · 117 across the 9 of their papers we have counts for
10 papers
Collective variables between large-scale states in turbulent convection
Priyanka Maity, Andreas Bittracher, Péter Koltai +1
The dynamics in a confined turbulent convection flow is dominated by multiple long-lived macroscopic circulation states, which are visited subsequently by the system in a Markov-ty…
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…
A weak characterization of slow variables in stochastic dynamical systems
Andreas Bittracher, Christof Schütte
We present a novel characterization of slow variables for continuous Markov processes that provably preserve the slow timescales. These slow variables are known as reaction coordin…
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.…
A kernel-based approach to molecular conformation analysis
Stefan Klus, Andreas Bittracher, Ingmar Schuster +1
We present a novel machine learning approach to understanding conformation dynamics of biomolecules. The approach combines kernel-based techniques that are popular in the machine l…
Data-driven Computation of Molecular Reaction Coordinates
Andreas Bittracher, Ralf Banisch, Christof Schütte
The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics is characterized by rare or slow transitio…
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…
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…
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…