TY - THES A1 - Rabben, Robert Julian T1 - Bestimmung invarianter Unterräume des Koopman-Operators einer Overdamped Langevin-Dynamik mithilfe eines Muli-Layer Neural Networks Y1 - 2019 ER - TY - THES A1 - Rabben, Robert Julian T1 - Ein holistischer Ansatz zur Analyse molekularer Konformationen auf der Basis von ISOKANN Y1 - 2022 ER - TY - JOUR A1 - Rabben, Robert Julian A1 - Ray, Sourav A1 - Weber, Marcus T1 - ISOKANN: Invariant subspaces of Koopman operators learned by a neural network JF - The Journal of Chemical Physics N2 - The problem of determining the rate of rare events in dynamical systems is quite well-known but still difficult to solve. Recent attempts to overcome this problem exploit the fact that dynamic systems can be represented by a linear operator, such as the Koopman operator. Mathematically, the rare event problem comes down to the difficulty in finding invariant subspaces of these Koopman operators K. In this article, we describe a method to learn basis functions of invariant subspaces using an artificial neural Network. Y1 - 2020 U6 - https://doi.org/10.1063/5.0015132 VL - 153 IS - 11 SP - 114109 ER - TY - JOUR A1 - Sikorski, Alexander A1 - Rabben, Robert Julian A1 - Chewle, Surahit A1 - Weber, Marcus T1 - Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions N2 - 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 produce useful trajectories, obtaining macroscopic information directly from microstate data presents significant challenges. This paper addresses this gap by introducing the concept of membership functions being the macrostates themselves. We derive equations for the holding times of these macrostates and demonstrate their consistency with the classical definition. Furthermore, we discuss the application of the ISOKANN method for learning these quantities from simulation data. In addition, we present a novel method for extracting transition paths based on the ISOKANN results and demonstrate its efficacy by applying it to simulations of the 𝜇-opioid receptor. With this approach we provide a new perspective on analyzing the macroscopic behaviour of Markov systems. Y1 - 2024 ER -