@article{EncisoSchuetteDelleSite2015, author = {Enciso, Marta and Sch{\"u}tte, Christof and Delle Site, Luigi}, title = {Influence of pH and sequence in peptide aggregation via molecular simulation}, volume = {143}, journal = {Journal of Chemical Physics}, number = {24}, doi = {https://doi.org/10.1063/1.4935707}, year = {2015}, language = {en} } @article{SchuetteSarich2015, author = {Sch{\"u}tte, Christof and Sarich, Marco}, title = {A Critical Appraisal of Markov State Models}, volume = {224}, journal = {The European Physical Journal Special Topics}, number = {12}, doi = {10.1140/epjst/e2015-02421-0}, pages = {2445 -- 2462}, year = {2015}, abstract = {Markov State Modelling as a concept for a coarse grained description of the essential kinetics of a molecular system in equilibrium has gained a lot of atten- tion recently. The last 10 years have seen an ever increasing publication activity on how to construct Markov State Models (MSMs) for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecu- lar sensors to molecular aggregation. Simultaneously the accompanying theory behind MSM building and approximation quality has been developed well be- yond the concepts and ideas used in practical applications. This article reviews the main theoretical results, provides links to crucial new developments, outlines the full power of MSM building today, and discusses the essential limitations still to overcome.}, language = {en} } @misc{BittracherBanischSchuette2017, author = {Bittracher, Andreas and Banisch, Ralf and Sch{\"u}tte, Christof}, title = {Data-driven Computation of Molecular Reaction Coordinates}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66179}, year = {2017}, abstract = {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.}, language = {en} } @article{WulkowKoltaiSunkaraetal.2021, author = {Wulkow, Niklas and Koltai, P{\´e}ter and Sunkara, Vikram and Sch{\"u}tte, Christof}, title = {Data-driven modelling of nonlinear dynamics by barycentric coordinates and memory}, journal = {J. Stat. Phys.}, arxiv = {http://arxiv.org/abs/2112.06742}, year = {2021}, abstract = {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.}, language = {en} } @article{SchuetteKlusHartmann2023, author = {Sch{\"u}tte, Christof and Klus, Stefan and Hartmann, Carsten}, title = {Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning}, volume = {32}, journal = {Acta Numerica}, doi = {10.1017/S0962492923000016}, pages = {517 -- 673}, year = {2023}, abstract = {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.}, language = {en} } @article{GelssKlusSchusteretal.2021, author = {Gelss, Patrick and Klus, Stefan and Schuster, Ingmar and Sch{\"u}tte, Christof}, title = {Feature space approximation for kernel-based supervised learning}, volume = {221}, journal = {Knowledge-Based Sytems}, publisher = {Elsevier}, doi = {https://doi.org/10.1016/j.knosys.2021.106935}, year = {2021}, language = {en} } @misc{SchuetteKlusHartmann2022, author = {Sch{\"u}tte, Christof and Klus, Stefan and Hartmann, Carsten}, title = {Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88637}, year = {2022}, abstract = {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.}, language = {en} } @article{SikorskiNiknejadWeberetal.2024, author = {Sikorski, Alexander and Niknejad, Amir and Weber, Marcus and Donati, Luca}, title = {Tensor-SqRA: Modeling the transition rates of interacting molecular systems in terms of potential energies}, volume = {160}, journal = {Journal of Chemical Physics}, arxiv = {http://arxiv.org/abs/2311.09779}, doi = {10.1063/5.0187792}, pages = {104112}, year = {2024}, abstract = {Estimating the rate of rare conformational changes in molecular systems is one of the goals of molecular dynamics simulations. In the past few decades, a lot of progress has been done in data-based approaches toward this problem. In contrast, model-based methods, such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article, we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the projected rate estimation, a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA.}, language = {en} } @inproceedings{SikorskiRabbenChewleetal.2025, author = {Sikorski, Alexander and Rabben, Robert Julian and Chewle, Surahit and Weber, Marcus}, title = {Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions}, booktitle = {Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023}, editor = {Fackeldey, K.}, publisher = {De Gruyter}, arxiv = {http://arxiv.org/abs/2404.10523}, doi = {10.1515/9783111376776-004}, pages = {41 -- 58}, year = {2025}, abstract = {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.}, language = {en} } @misc{ZhangSchuette2017, author = {Zhang, Wei and Sch{\"u}tte, Christof}, title = {Reliable approximation of long relaxation timescales in molecular dynamics}, issn = {1438-0064}, doi = {10.3390/e19070367}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63718}, year = {2017}, abstract = {Many interesting rare events in molecular systems like ligand association, protein folding or con- formational changes happen on timescales that often are not accessible by direct numerical simulation. Therefore rare event approximation approaches like interface sampling, Markov state model building or advanced reaction coordinate based free energy estimation have attracted huge attention recently. In this article we analyze the reliability of such approaches: How precise is an estimate of long relaxation timescales of molecular systems resulting from various forms of rare event approximation methods? Our results give a theoretical answer to this question by relating it with the transfer operator approach to molecular dynamics. By doing so they also allow for understanding deep connections between the different approaches.}, language = {en} }