TY - GEN A1 - Niemann, Jan-Hendrik A1 - Schütte, Christof A1 - Klus, Stefan T1 - Simulation data: Data-driven model reduction of agent-based systems using the Koopman generator T2 - PLOS ONE Y1 - 2021 U6 - https://doi.org/http://doi.org/10.5281/zenodo.4522119 N1 - This repository contains the simulation data for the article "Data-driven model reduction of agent-based systems using the Koopman generator" by Jan-Hendrik Niemann, Stefan Klus and Christof Schütte. The archive complete_voter_model.zip contains the simulation results for the extended voter model on a complete graph for the parameters given in the corresponding txt-files to learn a reduced SDE model. The files are of the form [types, time steps, samples, training points].The archive dependency.zip contains additional simulation results of the form [types, time steps, samples, training points] to learn a reduced SDE model. The parameters used are given in the corresponding txt-files.The archive random_voter_model.zip contains the simulation results to learn a reduced SDE model for the given adjacency matrix within the archive. The file aggregate_state is of the form [training points, types, time steps, samples]. The file full_state is of the form [training points, agents, time steps, samples].The archive predator_prey_model.zip contains the simulation results to learn a reduced SDE model and calculation of the mean value of the agent-based model. The data is of the form [types, time steps, samples, training points] and [samples, time steps, types].The archive two_clustered_voter_model.zip contains the simulation results for the extended voter model on a graph with two clusters for the given adjacency matrices to learn a reduced SDE model. The file aggregate_state is of the form [training points, types, time steps, samples]. The file full_state is of the form [training points, agents, time steps, samples]. VL - 16 IS - 5 ER - TY - JOUR A1 - del Razo, Mauricio A1 - Frömberg, Daniela A1 - Straube, Arthur A1 - Schütte, Christof A1 - Höfling, Felix A1 - Winkelmann, Stefanie T1 - A probabilistic framework for particle-based reaction–diffusion dynamics using classical Fock space representations JF - Letters in Mathematical Physics Y1 - 2022 U6 - https://doi.org/10.1007/s11005-022-01539-w VL - 112 IS - 49 ER - TY - JOUR A1 - Straube, Arthur A1 - Winkelmann, Stefanie A1 - Schütte, Christof A1 - Höfling, Felix T1 - Stochastic pH oscillations in a model of the urea–urease reaction confined to lipid vesicles JF - J. Phys. Chem. Lett. N2 - The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators. Y1 - 2021 U6 - https://doi.org/10.1021/acs.jpclett.1c03016 VL - 12 SP - 9888 EP - 9893 ER - TY - JOUR A1 - Ribera Borrell, Enric A1 - Quer, Jannes A1 - Richter, Lorenz A1 - Schütte, Christof T1 - Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics JF - SIAM Journal on Scientific Computing (SISC) N2 - Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings. KW - importance sampling KW - stochastic optimal control KW - rare event simulation KW - metastability KW - neural networks KW - metadynamics Y1 - 2023 U6 - https://doi.org/10.1137/22M1503464 VL - 89 IS - 1 ER - TY - JOUR A1 - Helfmann, Luzie A1 - Conrad, Natasa Djurdjevac A1 - Lorenz-Spreen, Philipp A1 - Schütte, Christof T1 - Modelling opinion dynamics under the impact of influencer and media strategies JF - Scientific Reports N2 - Digital communication has made the public discourse considerably more complex, and new actors and strategies have emerged as a result of this seismic shift. Aside from the often-studied interactions among individuals during opinion formation, which have been facilitated on a large scale by social media platforms, the changing role of traditional media and the emerging role of "influencers" are not well understood, and the implications of their engagement strategies arising from the incentive structure of the attention economy even less so. Here we propose a novel opinion dynamics model that accounts for these different roles, namely that media and influencers change their own positions on slower time scales than individuals, while influencers dynamically gain and lose followers. Numerical simulations show the importance of their relative influence in creating qualitatively different opinion formation dynamics: with influencers, fragmented but short-lived clusters emerge, which are then counteracted by more stable media positions. Mean-field approximations by partial differential equations reproduce this dynamic. Based on the mean-field model, we study how strategies of influencers to gain more followers can influence the overall opinion distribution. We show that moving towards extreme positions can be a beneficial strategy for influencers to gain followers. Finally, we demonstrate that optimal control strategies allow other influencers or media to counteract such attempts and prevent further fragmentation of the opinion landscape. Our modelling framework contributes to better understanding the different roles and strategies in the increasingly complex information ecosystem and their impact on public opinion formation. Y1 - 2023 U6 - https://doi.org/10.1038/s41598-023-46187-9 VL - 13 SP - 19375 ER - TY - JOUR A1 - Ernst, Ariane A1 - Unger, Nathalie A1 - Schütte, Christof A1 - Walter, Alexander A1 - Winkelmann, Stefanie T1 - Rate-limiting recovery processes in neurotransmission under sustained stimulation JF - Mathematical Biosciences N2 - At chemical synapses, an arriving electric signal induces the fusion of vesicles with the presynaptic membrane, thereby releasing neurotransmitters into the synaptic cleft. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. Of central interest is the question which of the two restoration steps acts as the limiting factor during neurotrans-mission under high-frequency sustained stimulation. In order to investigate this question, we introduce a novel non-linear reaction network which involves explicit recovery steps for both the vesicles and the release sites, and includes the induced time-dependent output current. The associated reaction dynamics are formulated by means of ordinary differential equations (ODEs), as well as via the associated stochastic jump process. While the stochastic jump model describes a single release site, the average over many release sites is close to the ODE solution and shares its periodic structure. The reason for this can be traced back to the insight that recovery dynamics of vesicles and release sites are statistically almost independent. A sensitivity analysis on the recovery rates based on the ODE formulation reveals that neither the vesicle nor the release site recovery step can be identified as the essential rate-limiting step but that the rate- limiting feature changes over the course of stimulation. Under sustained stimulation the dynamics given by the ODEs exhibit transient dynamics leading from an initial depression of the postsynaptic response to an asymptotic periodic orbit, while the individual trajectories of the stochastic jump model lack the oscillatory behavior an asymptotic periodicity of the ODE-solution. Y1 - 2023 U6 - https://doi.org/10.1016/j.mbs.2023.109023 VL - 362 ER - TY - JOUR A1 - Secker, Christopher A1 - Fackeldey, Konstantin A1 - Weber, Marcus A1 - Ray, Sourav A1 - Gorgulla, Christoph A1 - Schütte, Christof T1 - Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists JF - Journal of Cheminformatics N2 - Opioids are essential pharmaceuticals due to their analgesic properties, however, lethal side effects, addiction, and opioid tolerance are extremely challenging. The development of novel molecules targeting the μ-opioid receptor (MOR) in inflamed, but not in healthy tissue, could significantly reduce these unwanted effects. Finding such novel molecules can be achieved by maximizing the binding affinity to the MOR at acidic pH while minimizing it at neutral pH, thus combining two conflicting objectives. Here, this multi-objective optimal affinity approach is presented, together with a virtual drug discovery pipeline for its practical implementation. When applied to finding pH-specific drug candidates, it combines protonation state-dependent structure and ligand preparation with high-throughput virtual screening. We employ this pipeline to characterize a set of MOR agonists identifying a morphine-like opioid derivative with higher predicted binding affinities to the MOR at low pH compared to neutral pH. Our results also confirm existing experimental evidence that NFEPP, a previously described fentanyl derivative with reduced side effects, and recently reported β-fluorofentanyls and -morphines show an increased specificity for the MOR at acidic pH when compared to fentanyl and morphine. We further applied our approach to screen a >50K ligand library identifying novel molecules with pH-specific predicted binding affinities to the MOR. The presented differential docking pipeline can be applied to perform multi-objective affinity optimization to identify safer and more specific drug candidates at large scale. Y1 - 2023 U6 - https://doi.org/10.1186/s13321-023-00746-4 VL - 15 ER - TY - JOUR A1 - Carderera, Alejandro A1 - Pokutta, Sebastian A1 - Schütte, Christof A1 - Weiser, Martin T1 - An efficient first-order conditional gradient algorithm in data-driven sparse identification of nonlinear dynamics to solve sparse recovery problems under noise JF - Journal of Computational and Applied Mathematics N2 - 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. The discovery of governing equations from data thus has the potential to transform data-rich fields where well-established dynamical models remain unknown. This work contributes to the recent trend in data-driven sparse identification of nonlinear dynamics of finding the best sparse fit to observational data in a large library of potential nonlinear models. We propose an efficient first-order Conditional Gradient algorithm for solving the underlying optimization problem. In comparison to the most prominent alternative algorithms, the new algorithm shows significantly improved performance on several essential issues like sparsity-induction, structure-preservation, noise robustness, and sample efficiency. We demonstrate these advantages on several dynamics from the field of synchronization, particle dynamics, and enzyme chemistry. Y1 - 2021 ER - TY - JOUR A1 - Wulkow, Niklas A1 - Telgmann, Regina A1 - Hungenberg, Klaus-Dieter A1 - Schütte, Christof A1 - Wulkow, Michael T1 - Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples JF - Macromolecular Theory and Simulations N2 - Two different approaches to parameter estimation (PE) in the context of polymerization are introduced, refined, combined, and applied. The first is classical PE where one is interested in finding parameters which minimize the distance between the output of a chemical model and experimental data. The second is Bayesian PE allowing for quantifying parameter uncertainty caused by experimental measurement error and model imperfection. Based on detailed descriptions of motivation, theoretical background, and methodological aspects for both approaches, their relation are outlined. The main aim of this article is to show how the two approaches complement each other and can be used together to generate strong information gain regarding the model and its parameters. Both approaches and their interplay in application to polymerization reaction systems are illustrated. This is the first part in a two-article series on parameter estimation for polymer reaction kinetics with a focus on theory and methodology while in the second part a more complex example will be considered. Y1 - 2021 U6 - https://doi.org/10.1002/mats.202100017 VL - 30 ER - TY - JOUR A1 - del Razo, Mauricio J. A1 - Dibak, Manuel A1 - Schütte, Christof A1 - Noé, Frank T1 - Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics JF - The Journal of Chemical Physics Y1 - 2021 U6 - https://doi.org/10.1063/5.0060314 VL - 155 IS - 12 ER - TY - JOUR A1 - Gelss, Patrick A1 - Klus, Stefan A1 - Schuster, Ingmar A1 - Schütte, Christof T1 - Feature space approximation for kernel-based supervised learning JF - Knowledge-Based Sytems Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1016/j.knosys.2021.106935 VL - 221 PB - Elsevier ER - TY - JOUR A1 - Bittracher, Andreas A1 - Moschner, Johann A1 - Koksch, Beate A1 - Netz, Roland A1 - Schütte, Christof T1 - Exploring the locking stage of NFGAILS amyloid fibrillation via transition manifold analysis JF - The European Physical Journal B Y1 - 2021 U6 - https://doi.org/10.1140/epjb/s10051-021-00200-0 VL - 94 ER - TY - JOUR A1 - Helfmann, Luzie A1 - Heitzig, Jobst A1 - Koltai, Péter A1 - Kurths, Jürgen A1 - Schütte, Christof T1 - Statistical analysis of tipping pathways in agent-based models JF - Eur. Phys. J. Spec. Top. N2 - Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach. Y1 - 2021 U6 - https://doi.org/10.1140/epjs/s11734-021-00191-0 VL - 230 SP - 3249 EP - 3271 ER - TY - JOUR A1 - Sikorski, Alexander A1 - Weber, Marcus A1 - Schütte, Christof T1 - The Augmented Jump Chain JF - Advanced Theory and Simulations N2 - 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 physical systems or non-autonomous simulation processes are becoming more and more important. A representation of non-autonomous Markov jump processes is presented as autonomous Markov chains on space-time. Augmenting the spatial information of the embedded Markov chain by the temporal information of the associated jump times, the so-called augmented jump chain is derived. The augmented jump chain inherits the sparseness of the infinitesimal generator of the original process and therefore provides a useful tool for studying time-dependent dynamics even in high dimensions. Furthermore, possible generalizations and applications to the computation of committor functions and coherent sets in the non-autonomous setting are discussed. After deriving the theoretical foundations, the concepts with a proof-of-concept Galerkin discretization of the transfer operator of the augmented jump chain applied to simple examples are illustrated. Y1 - 2021 U6 - https://doi.org/10.1002/adts.202000274 VL - 4 IS - 4 PB - Wiley-VCH ER - TY - GEN A1 - Schütte, Christof A1 - Klus, Stefan A1 - Hartmann, Carsten T1 - Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning N2 - One of the main challenges in molecular dynamics is overcoming the “timescale barrier”, a phrase used to describe that in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, not even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics, and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behavior on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory as well as the algorithmic development from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in MD. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject. T3 - ZIB-Report - 22-25 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88637 SN - 1438-0064 ER -