5 papers
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…
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…