@article{HartmannSchuetteKalibaevaetal.2009, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Kalibaeva, G. and Pierro, M. and Ciccotti, Giovanni}, title = {Fast Simulation of Polymer Chains}, volume = {130}, journal = {J. Chem. Phys.}, doi = {10.1063/1.3110603}, pages = {144101}, year = {2009}, language = {en} } @article{LatorreMetznerHartmannetal.2011, author = {Latorre, J. and Metzner, Ph. and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {A Structure-preserving numerical discretization of reversible diffusions}, volume = {9}, journal = {Commun. Math. Sci.}, number = {4}, pages = {1051 -- 1072}, year = {2011}, language = {en} } @article{HartmannVulcanovSchuette2010, author = {Hartmann, Carsten and Vulcanov, V.-M. and Sch{\"u}tte, Christof}, title = {Balanced Truncation of Second Order Systems}, volume = {8}, journal = {Multiscale Model. Simul.}, number = {4}, doi = {10.1137/080732717}, pages = {1348 -- 1367}, year = {2010}, language = {en} } @article{LatorreHartmannSchuette2010, author = {Latorre, J. and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Free energy computation by controlled Langevin processes}, volume = {1}, journal = {Procedia Computer Science}, number = {1}, doi = {10.1016/j.procs.2010.04.179}, pages = {1591 -- 1600}, year = {2010}, language = {en} } @article{HartmannSchuetteCiccotti2010, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Ciccotti, Giovanni}, title = {On the linear response of mechanical systems with constraints}, volume = {132}, journal = {J. Chem. Phys.}, number = {11}, doi = {10.1063/1.3354126}, pages = {111103}, year = {2010}, language = {en} } @article{HartmannSchuette2008, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Balancing of partially-observed stochastic differential equations}, journal = {47th IEEE Conference on Decision and Control}, doi = {10.1109/CDC.2008.4739161}, pages = {4867 -- 4872}, year = {2008}, language = {en} } @article{HartmannSchuette2005, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {A Constrained Hybrid Monte-Carlo Algorithm and the Problem of Calculating the Free Energy in Several Variables}, volume = {85}, journal = {Z. Angew. Math. Mech.}, number = {10}, doi = {10.1002/zamm.200410218}, pages = {700 -- 710}, year = {2005}, language = {en} } @article{HartmannSchuette2005, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {A Geometric Approach to Constrained Molecular Dynamics and Free Energy}, volume = {3}, journal = {Comm. Math. Sci.}, number = {1}, pages = {1 -- 20}, year = {2005}, language = {en} } @article{SchuetteWalterHartmannetal.2004, author = {Sch{\"u}tte, Christof and Walter, J. and Hartmann, Carsten and Huisinga, Wilhelm}, title = {An Averaging Principle for Fast Degrees of Freedom Exhibiting Long-Term Correlations}, volume = {2}, journal = {Multiscale Model. Simul.}, number = {3}, doi = {10.1137/030600308}, pages = {501 -- 526}, year = {2004}, language = {en} } @article{HartmannSchuette2007, author = {Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Comment on Two Distinct Notions of Free Energy}, volume = {228}, journal = {Physica D}, number = {1}, doi = {10.1016/j.physd.2007.02.006}, pages = {59 -- 63}, year = {2007}, language = {en} } @article{HorenkoHartmannSchuetteetal.2007, author = {Horenko, Illia and Hartmann, Carsten and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {Data-based Parameter Estimation of Generalized Multidimensional Langevin Processes}, volume = {76}, journal = {Phys. Rev. E}, number = {01}, doi = {10.1103/PhysRevE.76.016706}, pages = {016706}, year = {2007}, language = {en} } @misc{ZhangHartmannSchuette2016, author = {Zhang, Wei and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Effective Dynamics Along Given Reaction Coordinates, and Reaction Rate Theory}, issn = {1438-0064}, doi = {10.1039/C6FD00147E}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59706}, year = {2016}, abstract = {In molecular dynamics and related fields one considers dynamical descriptions of complex systems in full (atomic) detail. In order to reduce the overwhelming complexity of realistic systems (high dimension, large timescale spread, limited computational resources) the projection of the full dynamics onto some reaction coordinates is examined in order to extract statistical information like free energies or reaction rates. In this context, the effective dynamics that is induced by the full dynamics on the reaction coordinate space has attracted considerable attention in the literature. In this article, we contribute to this discussion: We first show that if we start with an ergodic diffusion processes whose invariant measure is unique then these properties are inherited by the effective dynamics. Then, we give equations for the effective dynamics, discuss whether the dominant timescales and reaction rates inferred from the effective dynamics are accurate approximations of such quantities for the full dynamics, and compare our findings to results from approaches like Zwanzig-Mori, averaging, or homogenization. Finally, by discussing the algorithmic realization of the effective dynamics, we demonstrate that recent algorithmic techniques like the "equation-free" approach and the "heterogeneous multiscale method" can be seen as special cases of our approach.}, language = {en} } @article{ZhangHartmannSchuette2016, author = {Zhang, Wei and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Effective dynamics along given reaction coordinates, and reaction rate theory}, journal = {Faraday Discussions}, number = {195}, doi = {10.1039/C6FD00147E}, pages = {365 -- 394}, year = {2016}, language = {en} } @article{HartmannRichterSchuetteetal.2017, author = {Hartmann, Carsten and Richter, Lorenz and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Variational characterization of free energy: theory and algorithms}, volume = {19}, journal = {Entropy}, number = {11}, doi = {10.3390/e19110626}, pages = {626}, year = {2017}, language = {en} } @article{ZimperDjurdjevacHartmannetal.2025, author = {Zimper, Sebastian and Djurdjevac, Ana and Hartmann, Carsten and Sch{\"u}tte, Christof and Conrad, Natasa Djurdjevac}, title = {Mean-field optimal control with stochastic leaders}, arxiv = {http://arxiv.org/abs/2512.19201}, year = {2025}, abstract = {We consider interacting agent systems with a large number of stochastic agents (or particles) influenced by a fixed number of external stochastic lead agents. Such examples arise, for example in models of opinion dynamics, where a small number of leaders (influencers) can steer the behaviour of a large population of followers. In this context, we study a partial mean-field limit where the number of followers tends to infinity, while the number of leaders stays constant. The partial mean-field limit dynamics is then given by a McKean-Vlasov stochastic differential equation (SDE) for the followers, coupled to a controlled It{\^o}-SDE governing the dynamics of the lead agents. For a given cost functional that the lead agents seek to minimise, we show that the unique optimal control of the finite agent system convergences to the optimal control of the limiting system. This establishes that the low-dimensional control of the partial (mean-field) system provides an effective approximation for controlling the high-dimensional finite agent system. In addition, we propose a stochastic gradient descent algorithm that can efficiently approximate the mean-field control. Our theoretical results are illustrated on opinion dynamics model with lead agents, where the control objective is to drive the followers to reach consensus in finite time.}, language = {en} }