274 citations · 409 across the 17 of their papers we have counts for
17 papers
Effective Dynamics and Transition Pathways from Koopman-Inspired Neural Learning of Collective Variables
Alexander Sikorski, Luca Donati, Marcus Weber +1
The ISOKANN (Invariant Subspaces of Koopman Operators Learned by Artificial Neural Networks) framework provides a data-driven route to extract collective variables (CVs) and effect…
On-the-Fly Lifting of Coarse Reaction-Coordinate Paths to Full-Dimensional Transition Path Ensembles
Christof Schütte, Alexander Sikorski, Jakob Kresse +1
Effective dynamics on a low-dimensional collective-variable (CV) or latent space can be simulated far more cheaply than the underlying high-dimensional stochastic system, but explo…
Existence of Multilateral Nash equilibria for families of games
Matija Blagojevic, Christof Schütte
This paper introduces two fundamentally new concepts to game theory: multilateral Nash equilibria and families of games. Starting with non-cooperative games, we show how these noti…
Data-driven Reduction of Transfer Operators for Particle Clustering Dynamics
Nathalie Wehlitz, Grigorios A. Pavliotis, Christof Schütte +1
We develop an operator-based framework to coarse-grain interacting particle systems that exhibit clustering dynamics. Starting from the particle-based transfer operator, we first c…
Mean-field optimal control with stochastic leaders
Sebastian Zimper, Ana Djurdjevac, Carsten Hartmann +2
We consider interacting agent systems with a large number of stochastic agents influenced by a fixed number of external stochastic lead agents. Such settings arise, for example in…
Generative modeling of conditional probability distributions on the level-sets of collective variables
Fatima-Zahrae Akhyar, Wei Zhang, Gabriel Stoltz +1
Given a probability distribution in represented by data, we study in this paper the generative modeling of the corresponding conditional probability distribution…
Topology of the Generalized Nash Equilibrium Problem
Matija Blagojević, Christof Schütte
The Generalized Nash Equilibrium Problem refers to the question of the existence of a Nash equilibrium in an abstract economy. This model is due to Kenneth J. Arrow and Gerard Debr…
Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics
Wei Zhang, Christof Schütte
High-dimensional metastable molecular system can often be characterised by a few features of the system, i.e. collective variables (CVs). Thanks to the rapid advance in the area of…
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…
CINDy: Conditional gradient-based Identification of Non-linear Dynamics -- Noise-robust recovery
Alejandro Carderera, Sebastian Pokutta, Christof Schütte +1
Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies.…
Quantitative spectroscopy of single molecule interaction times
Horst-Holger Boltz, Alexei Sirbu, Nina Stelzer +3
Single molecule fluorescence tracking provides information at nm-scale and ms-temporal resolution about the dynamics and interaction of individual molecules in a biological environ…
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…
Data-driven approximation of the Koopman generator: Model reduction, system identification, and control
Stefan Klus, Feliks Nüske, Sebastian Peitz +3
We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode deco…
From interacting agents to density-based modeling with stochastic PDEs
Luzie Helfmann, Natasa Djurdjevac Conrad, Ana Djurdjevac +2
Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the syst…
Tensor-generated fractals: Using tensor decompositions for creating self-similar patterns
Patrick Gelß, Christof Schütte
The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as fin…
Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces
Mattes Mollenhauer, Ingmar Schuster, Stefan Klus +1
Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and…
Grand-canonical-like molecular-dynamics simulations by using an adaptive-resolution technique
Han Wang, Carsten Hartmann, Christof Schütte +1
In this work, we provide a detailed theoretical analysis, supported by numerical tests, of the reliability of the adaptive resolution simulation (AdResS) technique in sampling the…