4 citations · 11 across the 11 of their papers we have counts for
12 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…
Importance sampling of unbounded random stopping times: computing committor functions and exit rates without reweighting
Carsten Hartmann, Annika Jöster, Christof Schütte +2
Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare tra…
Revealing the Atomistic Mechanism of Rare Events in Molecular Dynamics
Jakob J. Kresse, Alexander Sikorski, Marcus Weber
Interpretable reaction coordinates are essential for understanding rare conformational transitions in molecular dynamics. The Atomistic Mechanism Of Rare Events in Molecular Dynami…
Voronoi Graph -- Improved raycasting and integration schemes for high dimensional Voronoi diagrams
Alexander Sikorski, Martin Heida
The computation of Voronoi Diagrams, or their dual Delauney triangulations is difficult in high dimensions. In a recent publication Polianskii and Pokorny propose an iterative rand…
Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions
Alexander Sikorski, Robert Julian Rabben, Surahit Chewle +1
Markov processes serve as foundational models in many scientific disciplines, such as molecular dynamics, and their simulation forms a common basis for analysis. While simulations…
Tensor-SqRA: Modeling the Transition Rates of Interacting Molecular Systems in terms of Potential Energies
Alexander Sikorski, Amir Niknejad, Marcus Weber +1
Estimating the rate of rare conformational changes in molecular systems is one of the goals of Molecular Dynamics simulations. In the past decades, a lot of progress has been done…
Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN
Alexander Sikorski, Enric Ribera Borrell, Marcus Weber
For stochastic diffusion processes the dominant eigenfunctions of the corresponding Koopman operator contain important information about the slow-scale dynamics, that is, about the…
Spectral clustering of Markov chain transition matrices with complex eigenvalues
Anna-Simone Frank, Alexander Sikorski, Susanna Röblitz
The Robust Perron Cluster Analysis (PCCA+) has become a popular spectral clustering algorithm for coarse-graining transition matrices of nearly decomposable Markov chains with tran…
The Augmented Jump Chain -- a sparse representation of time-dependent Markov jump processes
Alexander Sikorski, Marcus Weber, Christof Schütte
Modern methods of simulating molecular systems are based on the mathematical theory of Markov operators with a focus on autonomous equilibrated systems. However, non-autonomous phy…
Empirical Bayes Methods for Prior Estimation in Systems Medicine
Ilja Klebanov, Alexander Sikorski, Christof Schütte +1
One of the main goals of mathematical modeling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinica…
Objective Priors in the Empirical Bayes Framework
Ilja Klebanov, Alexander Sikorski, Christof Schütte +1
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating…