The dynamics of biomolecules show an inherent multiscale behaviour with cascades of timescales and strong interaction between them. Molecular dynamics (MD) simulations allow for analysis and understanding of this dynamical behaviour. However realistic simulations on timescales beyond milliseconds are still infeasible even on the most powerful computers, which renders the MD-based analysis of many important equilibrium processes related to biological function impossible. Driven by the recent progress in experimental techniques to manipulate single molecules, numerical nonequilibrium methods that attempt to bridge the timescale gap between the fastest random oscillations and the rare events that are related to the slowest function-related processes have gained enormous popularity. This project aims at exploiting ideas from stochastic control, in order to devise novel efficient importance sampling strategies based on optimal controls that speed up the sampling of the relevant rare events while giving statistical estimators with small variance and good convergence properties, beyond the asymptotic regime of large deviations theory.

Publications

2024
Connecting Stochastic Optimal Control and Reinforcement Learning Journal of Mathematical Physics, 65(8), 2024 Jannes Quer, Enric Ribera Borrell BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN Journal of Mathematical Physics, Vol.65, p. 013502, 2024 Alexander Sikorski, Enric Ribera Borrell, Marcus Weber BibTeX
arXiv
DOI
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Spectral clustering of Markov chain transition matrices with complex eigenvalues Journal of Computational and Applied Mathematics, Vol.444, p. 115791, 2024 Anna-Simone Frank, Alexander Sikorski, Susanna Röblitz BibTeX
arXiv
DOI
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
2023
Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics SIAM Journal on Scientific Computing (SISC), 89(1), 2023 Enric Ribera Borrell, Jannes Quer, Lorenz Richter, Christof Schütte BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning Acta Numerica, Vol.32, pp. 517-673, 2023 (preprint available as ZIB-Report 22-25) Christof Schütte, Stefan Klus, Carsten Hartmann PDF (ZIB-Report)
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
2022
Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension SIAM Journal on Numerical Analysis, 2022 (under review) Martin Heida, Alexander Sikorski, Marcus Weber BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
2021
Estimation of the Koopman Generator by Newton's Extrapolation Multiscale Modeling and Simulation, 19(2), pp. 758-774, 2021 Renata Sechi, Alexander Sikorski, Marcus Weber BibTeX
DOI
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics ZIB-Report 21-40 Enric Ribera Borrell, Jannes Quer, Lorenz Richter, Christof Schütte PDF
BibTeX
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
MSM building and projection for the analysis of time-resolved spectra Proceedings in Applied Mathematics and Mechanics, p. e202100102, 2021 Renata Sechi, Marcus Weber, Karsten Heyne BibTeX
DOI
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Markov models from the square root approximation of the Fokker–Planck equation: calculating the grid-dependent flux Journal of Physics: Condensed Matter, 33(11), p. 115902, 2021 Luca Donati, Marcus Weber, Bettina G. Keller BibTeX
DOI
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
2019
Ergodic SDEs on submanifolds and related numerical sampling schemes ESAIM: Mathematical Modelling and Numerical Analysis, 2019 Wei Zhang BibTeX
arXiv
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
From metastable to coherent sets - Time-discretization schemes Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol.29, pp. 012101-012101, 2019 (preprint available as ZIB-Report 17-74) Konstantin Fackeldey, Peter Koltai, Peter Nevir, Henning Rust, Axel Schild, Marcus Weber PDF (ZIB-Report)
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms Journal of Statistical Physics, 175(6), pp. 1214-1261, 2019 Carsten Hartmann, Christof Schütte, Wei Zhang BibTeX
arXiv
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates Multiscale Modeling and Simulation, pp. 1019-1051, 2019 Tony Lelièvre, Wei Zhang BibTeX
arXiv
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
2018
An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates SIAM Journal on Scientific Computing, 40(2), pp. A653-A670, 2018 (preprint available as ZIB-Report 17-09) Jannes Quer, Luca Donati, Bettina Keller, Marcus Weber PDF (ZIB-Report)
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Data-driven model reduction and transfer operator approximation Journal of Nonlinear Science, 28(3), pp. 985-1010, 2018 Stefan Klus, Feliks Nüske, Peter Koltai, Hao Wu, Ioannis Kevrekidis, Christof Schütte, Frank Noé BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Estimation of the infinitesimal generator by square-root approximation J. Phys.: Condens. Matter, 30(42), pp. 425201-425201, 2018 Luca Donati, Martin Heida, Bettina G. Keller, Marcus Weber BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Implications of PCCA+ in Molecular Simulation Computation, 6(1), p. 20, 2018 Marcus Weber BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Importance Sampling for metastable dynamical systems in molecular dynamics Doctoral thesis, Freie Universität Berlin, Marcus Weber (Advisor), 2018 Jannes Quer BibTeX
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Optimal control of Markov jump processes: Asymptotic analysis, algorithms and applications to the modeling of chemical reaction systems Communications in Mathematical Sciences, pp. 293-331, 2018 Wei Zhang, Carsten Hartmann, Max von Kleist BibTeX
DOI
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Optimal data-driven estimation of generalized Markov state models for non-equilibrium dynamics Computation, 6(1), 2018 Peter Koltai, Hao Wu, Frank Noé, Christof Schütte PDF
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Spectral Clustering for Non-Reversible Markov Chains Computational and Applied Mathematics, 37(5), pp. 6376-6391, 2018 (preprint available as ) Konstantin Fackeldey, Alexander Sikorski, Marcus Weber BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Supplementary: Implications of PCCA+ in Molecular Simulation 2018 Marcus Weber BibTeX
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
2017
Capturing the Dynamics of Hashtag-Communities International Workshop on Complex Networks and their Applications, pp. 401-413, 2017 Philipp Lorenz, Frederik Wolf, Jonas Braun, Natasa Djurdjevac Conrad, Philipp Hövel BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Eigenvalues of non-reversible Markov chains – A case study ZIB-Report 17-13 Marcus Weber PDF
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Finding Metastabilities in Reversible Markov Chains based on Incomplete Sampling: Case of Molecular Simulation Special Matrices, pp. 73-81, 2017 Konstantin Fackeldey, Amir Niknejad, Marcus Weber BibTeX
DOI
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
GenPCCA -- Markov State Models for Non-Equilibrium Steady States Big data clustering: Data preprocessing, variable selection, and dimension reduction. WIAS Report No. 29, pp. 70-80, 2017 Konstantin Fackeldey, Marcus Weber BibTeX
DOI
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Importance sampling in path space for diffusion processes with slow-fast variables Probability Theory and Related Fields, pp. 1-52, 2017 Carsten Hartmann, Christof Schütte, Marcus Weber, Wei Zhang BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Set-Free Markov State Model Building Journal of Chemical Physics, 146(12), 2017 (preprint available as ZIB-Report 17-10) Marcus Weber, Konstantin Fackeldey, Christof Schütte PDF (ZIB-Report)
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Some connections between importance sampling and enhanced sampling methods in molecular dynamics Journal of Chemical Physics, 2017 (accepted for publication, preprint available as ZIB-Report 17-30) Jannes Quer, Han Cheng Lie PDF (ZIB-Report)
BibTeX
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Utilizing hitting times for finding metastable sets in non-reversible Markov chains Journal of Comp. Dynamics, 2017 (under review, preprint available as ) S. Rüdrich, Marco Sarich, Christof Schütte BibTeX
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Variational characterization of free energy: theory and algorithms Entropy, 19(11), 2017 (preprint available as ) Carsten Hartmann, Lorenz Richter, Christof Schütte, Wei Zhang BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
2016
Model reduction algorithms for optimal control and importance sampling of diffusions Nonlinearity, 29(8), pp. 2298-2326, 2016 Carsten Hartmann, Christof Schütte, Wei Zhang BibTeX
DOI
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
On the numerical approximation of the Perron-Frobenius and Koopman operator Journal of Computational Dynamics, 3(1), pp. 51-77, 2016 Stefan Klus, Peter Koltai, Christof Schütte BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
The Monte Carlo Computation Error of Transition Probabilities Statistics & Probability Letters, Vol.118, pp. 163-170, 2016 (preprint available as ZIB-Report 16-37) Adam Nielsen PDF (ZIB-Report)
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
2015
Approximating and Clustering Markov Chains via Kullback-Leibler-Divergence Master's thesis, Freie Universität Berlin, Marcus Weber (Advisor), 2015 Christoph Lange BibTeX
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Computing the nearest reversible Markov chain Numerical Linear Algebra with Applications, 22(3), pp. 483-499, 2015 (preprint available as ) Adam Nielsen, Marcus Weber BibTeX
DOI
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Die Cross-Entropy-Methode für stochastische Optimierungsprobleme Master's thesis, Freie Universität Berlin, Marcus Weber (Advisor), 2015 Oliver Zwingel BibTeX
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Estimating exit rates in rare event dynamical systems via extrapolation ZIB-Report 15-54 Marcus Weber, Jannes Quer PDF
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Markov State Models and Molecular Alchemy Molecular Physics, 113(1), pp. 69-78, 2015 (preprint available as ) Christof Schütte, Adam Nielsen, Marcus Weber BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
2014
Applications of the cross-entropy method to importance sampling and optimal control of diffusions Siam Journal on Scientific Computing, 36(6), pp. A2654-A2672, 2014 (preprint available as ZIB-Report 14-10) Wei Zhang, Han Wang, Carsten Hartmann, Marcus Weber, Christof Schütte PDF (ZIB-Report)
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Building Markov State Models for Periodically Driven Non-Equilibrium Systems ZIB-Report 14-46 Han Wang, Christof Schütte PDF
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Markov Model Theory An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation, Vol.797, pp. 23-44, Gregory R. Bowman, Vijay S. Pande, Frank Noé (Eds.), Springer, 2014 Marco Sarich, Christof Schütte BibTeX
DOI
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Modularity revisited: A novel dynamics-based concept for decomposing complex networks Journal of Computational Dynamics, 1(1), pp. 191-212, 2014 Marco Sarich, Natasa Djurdjevac Conrad, Sharon Bruckner, Tim Conrad, Christof Schütte PDF
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
Molecular Dynamics Simulation Giovanni Ciccotti, Mauro Ferrario, Christof Schütte (Eds.), Multidisciplinary Digital Publishing Institute (MDPI), 2014 BibTeX
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
ZIBgridfree: Efficient Conformational Analysis by Partition-of-Unity Coupling Journal of Mathematical Chemistry, 52(3), pp. 781-804, 2014 (preprint available as ZIB-Report 13-58) Alexander Bujotzek, Ole Schütt, Adam Nielsen, Konstantin Fackeldey, Marcus Weber PDF (ZIB-Report)
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
2013
Markov State Models for Rare Events in Molecular Dynamics Entropy (Special Issue), 16(1), pp. 258-286, 2013 (preprint available as ) Marco Sarich, Ralf Banisch, Carsten Hartmann, Christof Schütte BibTeX
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Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing
2012
A Meshless Method for Conformational Analysis Master's thesis, Freie Universität Berlin, Marcus Weber (Advisor), 2012 Han Cheng Lie BibTeX
Probing Scales in Equilibrated Systems by Optimal Nonequilibrium Forcing