TY - GEN A1 - Osterland, Marc A1 - Benn, Andreas A1 - Prohaska, Steffen A1 - Schütte, Christof T1 - Single Cell Tracking in Phase-Contrast Microscopy T2 - EMBL Symposium 2015 - Seeing is Believing - Imaging the Processes of Life N2 - In this work, we developed an automatic algorithm to analyze cell migration in chemotaxis assays, based on phase-contrast time-lapse microscopy. While manual approaches are still widely used in recent publications, our algorithm is able to track hundreds of single cells per frame. The extracted paths are analysed with traditional geometrical approaches as well as diffusion-driven Markov state models (MSM). Based on these models, a detailed view on spatial and temporal effects is possible. Using our new approach on experimental data, we are able to distinguish between directed migration (e.g. towards a VEGF gradient) and random migration without favored direction. A calculation of the committor probabilities reveals that cells of the whole image area are more likely to migrate directly towards the VEGF than away from it during the first four hours. However, in absence of a chemoattractant, cells migrate more likely to their nearest image border. These conclusions are supported by the spatial mean directions. In a next step, the cell-cell interaction during migration and the migration of cell clusters will be analyzed. Furthermore, we want to observe phenotypical changes during migration based on fluorescence microscopy and machine learning. The algorithm is part of a collaborative platform which brings the experimental expertise of scientists from life sciences and the analytical knowledge of computer scientists together. This platform is built using web-based technologies with a responsive real-time user interface. All data, including raw and metadata as well as the accompanying results, will be stored in a secure and scalable compute cluster. The compute cluster provides sufficient space and computational power for modern image-based experiments and their analyses. Specific versions of data and results can be tagged to keep immutable records for archival. Y1 - 2015 ER - TY - GEN A1 - Koltai, Peter A1 - Ciccotti, Giovanni A1 - Schütte, Christof T1 - On metastability and Markov state models for non-stationary molecular dynamics BT - 2016 Editor's Choice of The Journal of Chemical Physics T2 - The Journal of Chemical Physics N2 - We utilize the theory of coherent sets to build Markov state models for non- equilibrium molecular dynamical systems. Unlike for systems in equilibrium, “meta- stable” sets in the non-equilibrium case may move as time evolves. We formalize this concept by relying on the theory of coherent sets, based on this we derive finite-time non-stationary Markov state models, and illustrate the concept and its main differences to equilibrium Markov state modeling on simple, one-dimensional examples. T3 - ZIB-Report - 16-11 KW - coherent set, KW - Markov state model KW - non-equilibrium molecular dynamics KW - metastability Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57869 SN - 1438-0064 VL - 174103 ET - 145 ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Weber, Marcus A1 - Schütte, Christof T1 - Finding dominant structures of nonreversible Markov processes JF - Multiscale Modeling and Simulation Y1 - 2016 U6 - https://doi.org/10.1137/15M1032272 VL - 14 IS - 4 SP - 1319 EP - 1340 ER - TY - GEN A1 - Gupta, Pooja A1 - Röblitz, Susanna A1 - Krause, Carola A1 - Knaus, Petra A1 - Schütte, Christof T1 - Mathematical modeling of the Smad and Non-Smad BMP signaling pathways in context of cell density T2 - Computational Models in biology and medicine, 2013, Dresden, Germany Y1 - 2013 ER - TY - CHAP A1 - Gupta, Pooja A1 - Krause, Carola A1 - Rikeit, Paul A1 - Röblitz, Susanna A1 - Knaus, Petra A1 - Schütte, Christof T1 - Modeling of the BMP mediated co-regulation of the Smad and Non-Smad pathways in the context of cell density T2 - 10th International BMP conference, 2014, Berlin, Germany Y1 - 2014 ER - TY - JOUR A1 - Gul, Raheem A1 - Schütte, Christof A1 - Bernhard, Stefan T1 - Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries JF - Applied Mathematical Modelling Y1 - 2016 U6 - https://doi.org/10.1016/j.apm.2016.03.041 ER - TY - GEN A1 - Bittracher, Andreas A1 - Banisch, Ralf A1 - Schütte, Christof T1 - Data-driven Computation of Molecular Reaction Coordinates N2 - The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics is characterized by rare or slow transition events. In a recent publication, the authors identified a condition under which such reaction coordinates exist - the existence of a so-called transition manifold - and proposed a numerical method for their point-wise computation that relies on short bursts of MD simulations. This article represents an extension of the method towards practical applicability in computational chemistry. It describes an alternative computational scheme that instead relies on more commonly available types of simulation data, such as single long molecular trajectories, or the push-forward of arbitrary canonically-distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates, that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, that computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated on a realistic peptide system. T3 - ZIB-Report - 17-77 KW - reaction coordinate KW - coarse graining KW - transition manifold KW - transfer operator KW - Galerkin method KW - meshfree basis KW - data-driven Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66179 SN - 1438-0064 ER - TY - THES A1 - Schütte, Christof T1 - Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules N2 - The function of many important biomolecules comes from their dynamic properties and their ability to switch between different {\em conformations}. In a conformation, the large scale geometric structure of the molecule is understood to be conserved, whereas on smaller scales the system may well rotate, oscillate or fluctuate. In a recent article [J. Comp. Phys., 151,1 (1999)], the present author and coworkers demonstrated that (a) conformations can be understood as almost invariant sets of some Markov chain being defined via the Hamiltonian system governing the molecular dynamics and that (b) these sets can efficiently be computed via eigenvectors of the corresponding Markov operator. The persent manuscript reviews the mathematical modelling steps behind the novel concept, includes a rigorous analytical justification of this approach and especially of the numerical details of the algorithm, and illustrates its performance when applied to realistic molecular systems. T3 - ZIB-Report - SC-99-18 KW - biochemical conformation KW - almost invariant set KW - Markov chain KW - Hamiltonian system KW - Markov operator KW - quasi-compact operator KW - Perron root KW - Perron- Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4063 ER - TY - GEN A1 - Fischer, Alexander A1 - Schütte, Christof A1 - Deuflhard, Peter A1 - Cordes, Frank T1 - Hierarchical Uncoupling-Coupling of Metastable Conformations N2 - Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. UCMC aims at avoiding the typical metastable or trapping behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. Therefore, the state space of the chain has to be hierarchically decomposed into its metastable conformations. This is done by means of combining the technique of conformation analysis as recently introduced by the authors, and appropriate annealing strategies. We present a detailed examination of the uncoupling-coupling procedure which uncovers its theoretical background, and illustrates the hierarchical algorithmic approach. Furthermore, application of the UCMC algorithm to the $n$-pentane molecule allows us to discuss the effect of its crucial steps in a typical molecular scenario. T3 - ZIB-Report - 01-03 KW - almost invariant sets KW - bridge sampling KW - metastability KW - hierarchical annealing KW - hybrid Monte Carlo KW - $n$-pentane molecule KW - ratio of normalizing co Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6296 ER - TY - JOUR A1 - Wulkow, Niklas A1 - Koltai, Péter A1 - Sunkara, Vikram A1 - Schütte, Christof T1 - Data-driven modelling of nonlinear dynamics by barycentric coordinates and memory JF - J. Stat. Phys. N2 - 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 Euclidean space to convex polytopes and represent these projected states of a system in new, lower-dimensional coordinates denoting their position in the polytope. We then introduce a specific nonlinear transformation to construct a model of the dynamics in the polytope and to transform back into the original state space. To overcome the potential loss of information from the projection to a lower-dimensional polytope, we use memory in the sense of the delay-embedding theorem of Takens. By construction, our method produces stable models. We illustrate the capacity of the method to reproduce even chaotic dynamics and attractors with multiple connected components on various examples. Y1 - 2021 ER - TY - GEN A1 - Ernst, Ariane A1 - Schütte, Christof A1 - Sigrist, Stephan A1 - Winkelmann, Stefanie T1 - Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics N2 - Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal’s second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal. T3 - ZIB-Report - 21-15 KW - linear reaction networks KW - cross-correlation KW - neurotransmission Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82674 SN - 1438-0064 ER - TY - JOUR A1 - Ernst, Ariane A1 - Schütte, Christof A1 - Sigrist, Stephan A1 - Winkelmann, Stefanie T1 - Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics JF - Mathematical Biosciences N2 - Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal’s second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal. Y1 - 2022 U6 - https://doi.org/10.1016/j.mbs.2021.108760 VL - 343 ER - TY - JOUR A1 - Thies, Arne A1 - Sunkara, Vikram A1 - Ray, Sourav A1 - Wulkow, Hanna A1 - Celik, M. Özgür A1 - Yergöz, Fatih A1 - Schütte, Christof A1 - Stein, Christoph A1 - Weber, Marcus A1 - Winkelmann, Stefanie T1 - Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design JF - Scientific Reports N2 - We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account. Y1 - 2023 U6 - https://doi.org/10.1038/s41598-023-27699-w VL - 13 IS - 607 ER - TY - GEN A1 - Ray, Sourav A1 - Thies, Arne A1 - Sunkara, Vikram A1 - Wulkow, Hanna A1 - Celik, Özgür A1 - Yergöz, Fatih A1 - Schütte, Christof A1 - Stein, Christoph A1 - Weber, Marcus A1 - Winkelmann, Stefanie T1 - Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design N2 - Initiated by mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands in normal versus diseased (inflamed) environments, we previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. Uniquely, this design recognised that GPCRs function differently under pathological versus healthy conditions. We now present a novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels associated with parameters of inflamed tissue (pH, radicals). By means of molecular dynamics simulations, we also assessed qualitative changes of the reaction rates due to additional disulfide bridges inside the GPCR binding pocket and used these rates for stochastic simulations of the corresponding reaction jump process. The modelling results were validated with in vitro experiments measuring calcium currents and G-protein activation. We found markedly reduced G-protein dissociation and calcium channel inhibition induced by NFEPP at normal pH, and enhanced constitutive G-protein activation but lower probability of ligand binding with increasing radical concentrations. These results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account. T3 - ZIB-Report - 21-19 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82797 SN - 1438-0064 ER - TY - JOUR A1 - Montefusco, Alberto A1 - Schütte, Christof A1 - Winkelmann, Stefanie T1 - A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures JF - SIAM Journal on Applied Mathematics N2 - The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of reaction-diffusion partial differential equations. Analyzing and understanding the relation between different mathematical models for reaction-diffusion dynamics is a research topic of steady interest. In this work, we explore a route to the hydrodynamic limit of the RDME which uses gradient structures. Specifically, we elaborate on a method introduced in [J. Maas and A. Mielke, J. Stat. Phys., 181 (2020), pp. 2257–2303] in the context of well-mixed reaction networks by showing that, once it is complemented with an appropriate limit procedure, it can be applied to spatially extended systems with diffusion. Under the assumption of detailed balance, we write down a gradient structure for the RDME and use the method in order to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE. Y1 - 2023 U6 - https://doi.org/10.1137/22M1488831 VL - 83 IS - 2 SP - 837 EP - 861 ER - TY - JOUR A1 - Peppert, Felix A1 - von Kleist, Max A1 - Schütte, Christof A1 - Sunkara, Vikram T1 - On the Sufficient Condition for Solving the Gap-Filling Problem Using Deep Convolutional Neural Networks JF - IEEE Transactions on Neural Networks and Learning Systems N2 - Deep convolutional neural networks (DCNNs) are routinely used for image segmentation of biomedical data sets to obtain quantitative measurements of cellular structures like tissues. These cellular structures often contain gaps in their boundaries, leading to poor segmentation performance when using DCNNs like the U-Net. The gaps can usually be corrected by post-hoc computer vision (CV) steps, which are specific to the data set and require a disproportionate amount of work. As DCNNs are Universal Function Approximators, it is conceivable that the corrections should be obsolete by selecting the appropriate architecture for the DCNN. In this article, we present a novel theoretical framework for the gap-filling problem in DCNNs that allows the selection of architecture to circumvent the CV steps. Combining information-theoretic measures of the data set with a fundamental property of DCNNs, the size of their receptive field, allows us to formulate statements about the solvability of the gap-filling problem independent of the specifics of model training. In particular, we obtain mathematical proof showing that the maximum proficiency of filling a gap by a DCNN is achieved if its receptive field is larger than the gap length. We then demonstrate the consequence of this result using numerical experiments on a synthetic and real data set and compare the gap-filling ability of the ubiquitous U-Net architecture with variable depths. Our code is available at https://github.com/ai-biology/dcnn-gap-filling. Y1 - 2022 U6 - https://doi.org/10.1109/TNNLS.2021.3072746 VL - 33 IS - 11 SP - 6194 EP - 6205 ER - TY - JOUR A1 - Bittracher, Andreas A1 - Mollenhauer, Mattes A1 - Koltai, Péter A1 - Schütte, Christof T1 - Optimal Reaction Coordinates: Variational Characterization and Sparse Computation JF - Multiscale Modelling & Simulation N2 - 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 general variational characterization of optimal RCs and provide conditions for their existence. Optimal RCs are minimizers of a certain loss function, and reduced models based on them guarantee a good approximation of the statistical long-term properties of the original high-dimensional process. We show that for slow-fast systems, metastable systems, and other systems with known good RCs, the novel theory reproduces previous insight. Remarkably, for reversible systems, the numerical effort required to evaluate the loss function scales only with the variability of the underlying, low-dimensional mechanism, and not with that of the full system. The theory provided lays the foundation for an efficient and data-sparse computation of RCs via modern machine learning techniques. Y1 - 2023 U6 - https://doi.org/10.1137/21M1448367 VL - 21 IS - 2 SP - 449 EP - 488 ER - TY - JOUR A1 - Mollenhauer, Mattes A1 - Klus, Stefan A1 - Schütte, Christof A1 - Koltai, Péter T1 - Kernel Autocovariance Operators of Stationary Processes: Estimation and Convergence JF - Journal of Machine Learning Research N2 - We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the process under various conditions. In particular, we examine ergodic and strongly mixing processes and obtain several asymptotic results as well as finite sample error bounds. We provide applications of our theory in terms of consistency results for kernel PCA with dependent data and the conditional mean embedding of transition probabilities. Finally, we use our approach to examine the nonparametric estimation of Markov transition operators and highlight how our theory can give a consistency analysis for a large family of spectral analysis methods including kernel-based dynamic mode decomposition. Y1 - 2022 UR - https://jmlr.org/papers/v23/20-442.html VL - 23 IS - 327 SP - 1 EP - 34 ER - TY - GEN A1 - Helfmann, Luzie A1 - Djurdjevac Conrad, Natasa A1 - Lorenz-Spreen, Philipp A1 - Schütte, Christof T1 - Supplementary code for the paper Modelling opinion dynamics under the impact of influencer and media strategies N2 - This repository contains the Julia code accompanying the paper "Modelling opinion dynamics under the impact of influencer and media strategies", Scientific Reports, Vol.13, p. 19375, 2023. Y1 - 2023 U6 - https://doi.org/10.12752/9267 ER - TY - JOUR A1 - Wehlitz, Nathalie A1 - Sadeghi, Mohsen A1 - Montefusco, Alberto A1 - Schütte, Christof A1 - Pavliotis, Grigorios A. A1 - Winkelmann, Stefanie T1 - Approximating particle-based clustering dynamics by stochastic PDEs JF - SIAM Journal on Applied Dynamical Systems N2 - This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane mediated receptor dynamics on cell surfaces, we formulate a stochastic particle-based model for diffusion and pairwise interaction of particles, leading to intriguing clustering phenomena. Employing numerical simulation and cluster detection methods, we explore the approximation of the particle-based clustering dynamics through mean-field approaches. We find that SPDEs successfully reproduce spatiotemporal clustering dynamics, not only in the initial cluster formation period, but also on longer time scales where the successive merging of clusters cannot be tracked by deterministic mean-field models. The computational efficiency of the SPDE approach allows us to generate extensive statistical data for parameter estimation in a simpler model that uses a Markov jump process to capture the temporal evolution of the cluster number. Y1 - 2025 U6 - https://doi.org/10.1137/24M1676661 VL - 24 IS - 2 SP - 1231 EP - 1250 ER - TY - JOUR A1 - Kostré, Margarita A1 - Djurdjevac Conrad, Natasa A1 - Schütte, Christof A1 - Sunkara, Vikram T1 - Exploration of Particle Swarm Optimisation Algorithm with Divergent Parameters JF - Natural Computing Y1 - 2024 ER - TY - JOUR A1 - Regényi, Enikő A1 - Mashreghi, Mir-Farzin A1 - Schütte, Christof A1 - Sunkara, Vikram T1 - Exploring transcription modalities from bimodal, single-cell RNA sequencing data JF - NAR Genomics and Bioinformatics N2 - Abstract There is a growing interest in generating bimodal, single-cell RNA sequencing (RNA-seq) data for studying biological pathways. These data are predominantly utilized in understanding phenotypic trajectories using RNA velocities; however, the shape information encoded in the two-dimensional resolution of such data is not yet exploited. In this paper, we present an elliptical parametrization of two-dimensional RNA-seq data, from which we derived statistics that reveal four different modalities. These modalities can be interpreted as manifestations of the changes in the rates of splicing, transcription or degradation. We performed our analysis on a cell cycle and a colorectal cancer dataset. In both datasets, we found genes that are not picked up by differential gene expression analysis (DGEA), and are consequently unnoticed, yet visibly delineate phenotypes. This indicates that, in addition to DGEA, searching for genes that exhibit the discovered modalities could aid recovering genes that set phenotypes apart. For communities studying biomarkers and cellular phenotyping, the modalities present in bimodal RNA-seq data broaden the search space of genes, and furthermore, allow for incorporating cellular RNA processing into regulatory analyses. Y1 - 2024 U6 - https://doi.org/10.1093/nargab/lqae179 SN - 2631-9268 VL - 6 IS - 4 PB - Oxford University Press (OUP) ER - TY - CHAP A1 - Ribera Borrell, Enric A1 - Richter, Lorenz A1 - Schütte, Christof T1 - Reinforcement Learning with Random Time Horizons T2 - Proceedings of the 42nd International Conference on Machine Learning Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v267/main/assets/borrell25a/borrell25a.pdf VL - 267 SP - 5101 EP - 5123 ER - TY - GEN 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 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. T3 - ZIB-Report - 21-40 KW - importance sampling KW - stochastic optimal control KW - rare event simulation KW - metastability KW - neural networks KW - metadynamics Y1 - 2021 SN - 1438-0064 ER - TY - JOUR A1 - Schütte, Christof A1 - Klus, Stefan A1 - Hartmann, Carsten T1 - Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning JF - Acta Numerica N2 - One of the main challenges in molecular dynamics is overcoming the ‘timescale barrier’: in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, 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 behaviour 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 molecular dynamics. 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. Y1 - 2023 U6 - https://doi.org/10.1017/S0962492923000016 VL - 32 SP - 517 EP - 673 ER -