• Computationally feasible bounds for the free energy of nonequilibrium steady states, applied to simple models of heat conduction
    L. Delle Site, C. Hartmann.
    submitted to Mol. Phys., 2024 (arXiv preprint)
  • Risk-neutral limit of adaptive importance sampling of random stopping times
    C. Hartmann, A. Jöster.
    submitted to 26th International Symposium on Mathematical Theory of Networks and Systems, 2024 (arXiv preprint)
  • Scaling law for the size dependence of a short-ranged quantum gas
    L. Delle Site, C. Hartmann.
    Phys. Rev. A 109, 022209. 2024 (arXiv preprint)
  • Nonasymptotic bounds for suboptimal importance sampling
    C. Hartmann, L. Richter
    to appear in SIAM-ASA J. Uncertain. Quant., 2024 (arXiv preprint)
  • Differentiability of G-neutral stochastic differential equations with respect to parameter.
    Z. Boumezbeur, H. Boutabia, A. Redjil, O. Kebiri.
    to appear in Random Oper. Stoch. Equ., 2024 (journal article)
  • Analysis and optimal control of a vaccinated pandemic COVID-19 model.
    S.M. Lalaoui Ben Cherif, O. Balatif, O. Kebiri.
    to appear in J. Math. Sci., 2024 (journal article)
  • Infinite horizon RBSDEs with single L2-obstacle and applications.
    A. Almualim, M. Eddahbi, O. Kebiri, A. Sene.
    to appear in Open Mathematics 2024.
  • Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning
    Ch. Schütte, S. Klus, C. Hartmann.
    Acta Numerica 32, 517-673, 2023 (journal article)
  • Numerical Solutions of Stochastic Differential Equations with Jumps and Measurable Drifts
    M. Siddiqui, M. Eddahbi, O. Kebiri.
    Mathematics 11(17), 3755, 2023 (journal article)
  • Infinite Horizon Irregular Quadratic BSDE and Applications to Quadratic PDE and Epidemic Models with Singular Coefficients
    M. Eddahbi, O. Kebiri, A. Sene.
    Axioms 12(12), 1068, 2023 (journal article)
  • Fractional stochastic differential equations driven by G-Brownian motion with delays
    A. Saci, A. Redjil, H. Boutabia, O. Kebiri.
    Probab. Math. Stat. 43(1), 2023 (pdf of preprint)
  • Finite size effects and thermodynamic accuracy in many-particle systems
    B. Reible, J. Hille, C. Hartmann, L. Delle Site.
    Phys. Rev. Res. 5, 023156, 2023 (journal article)
  • On the existence and uniqueness of the solution to multifractional stochastic delay differential equation
    K. Bouguetof, Z. Mezdoud, O. Kebiri, C. Hartmann.
    submitted to Fract. Calc. Appl. Anal., 2023 (pdf of preprint)
  • Relaxed optimal control problem for a finite horizon G-SDE with delay and its application in economics
    O. Kebiri, N. Elgroud
    submitted to Fract. Calc. Appl. Anal., 2023 (arXiv preprint)
  • Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustness
    C. Hartmann, L. Richter
    to appear in: Artificial Intelligence – Limits and Prospects, P. Klimczak, Christer Petersen (eds.), Transcript, Bielefeld, 2023 (pdf of preprint)
  • Deep Learning for Solving Initial Path Optimization of Mean-Field Systems With Memory
    N. Agram, M. Grid, O. Kebiri, B. Øksendal.
    submitted, 2022 (SSRN-Preprint)
  • Two-sided Bogoliubov inequality to estimate finite-size effects in quantum molecular simulations
    B. Reible, C. Hartmann, L. Delle Site.
    Lett. Math. Phys. 112, 97, 2022 (journal article)
  • The relaxed maximum principle for G-stochastic control systems with controlled jumps
    H. Ben Gherbal , A. Redjil, O. Kebiri.
    Adv. Math. Sci. J. 11, 1313-1343, 2022 (journal article)
  • Long Short-Term Memory Neural Network for Temperature Prediction in Laser Powder Bed Additive Manufacturing
    A.M. Yarahmadi, M. Breuß, C. Hartmann
    In: Arai, K. (eds) Intelligent Systems and Applications. IntelliSys 2022. Lecture Notes in Networks and Systems, vol 544. Springer, Cham, 2023 (journal link)
  • Existence of relaxed optimal control for G-neutral stochastic functional differential equations with uncontrolled diffusion
    N. Elgroud, H. Boutabia, A. Redjil, O. Kebiri
    Bull. Inst. Math. Acad. Sinica 17, 143-172, 2022 (arXiv preprint)
  • Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces
    S. Becker, C. Hartmann, M. Redmann, L. Richter
    Stoch. Process. Appl. 149, 107-141, 2022 (arXiv preprint)
  • \(\alpha\)-Hypergeometric Uncertain Volatility Models and their Connection to 2BSDEs
    Z. Mezdoud, C. Hartmann, M. Riad Remita, O. Kebiri.
    Bull. Inst. Math. Acad. Sinica 16(3), 263-288,2021 (arXiv preprint)
  • Existence of relaxed stochastic optimal control for G-SDEs with controlled jumps
    A. Redjil, H.B. Gherbal, O. Kebiri.
    to appear in Stochastic Analysis and Applications, 2021 (journal link)
  • Choice of Damping Coefficient in Langevin Dynamics
    R.D. Skeel, C. Hartmann
    EPJ B Topical Issue "Recent progress and emerging trends in Molecular Dynamics" 94, 178, 2021 (pdf of article)
  • Reachability Analysis of Randomly Perturbed Hamiltonian Systems
    C. Hartmann, L. Neureither, M. Strehlau
    7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (LHMNC21), IFAC-Papers Online 54, 307-314, 2021 (arXiv preprint)
  • Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: a stochastic control approach
    T. Breiten, C. Hartmann, L. Neureither, U. Sharma
    J. Math. Phys. 62, 123302, 2021 (arXiv preprint)
  • Model reduction and uncertainty quantification of multiscale diffusions with parameter uncertainties using nonlinear expectations
    H. Bouanani, C. Hartmann, O. Kebiri
    submitted, 2021 (arXiv preprint)
  • Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
    N. Nüsken, L. Richter
    Partial Differ. Equ. Appl. 2, 48, 2021(arXiv preprint)
  • On the existence and uniqueness of solutions to forward backward stochastic differential equations driven by G-Brownian motion
    O. Kebiri, H. Bouanani, A. Kandouci
    Bull. Inst. Math. Acad. Sinica15, 217-236, 2020 (preprint)
  • VarGrad: A Low-Variance Gradient Estimator for Variational Inference
    L. Richter, A. Boustati, N. Nüsken, F.J.R. Ruiz, Ö.D. Akyildiz
    Advances in Neural Information Processing Systems 2020, 2020 (arXiv preprint)
  • Coarse-graining of non-reversible stochastic differential equations: quantitative results and connections to averaging
    C. Hartmann, L. Neureither, U. Sharma
    SIAM J. Math. Anal. 52(3), 2689-2733, 2020 (arXiv preprint)
  • Model reduction of controlled Fokker-Planck and Liouville-von Neumann equations
    P. Benner, T. Breiten, C. Hartmann and B. Schmidt
    J. Comput. Dynamics 7(1), 1-33, 2020 (pdf of preprint)
  • Gefangen in der Filterblase? Suchmaschinenergebnisse als Beispiel eines wissensbasierten Konsenses
    C. Hartmann
    In: P. Klimczak, Ch. Petersen, S. Schilling (Hrsg.), Maschinen der Kommunikation. Interdisziplinäre Perspektiven auf Technik und Gesellschaft im digitalen Zeitalter, pp. 45-62,  Springer Ars Digitalis, 2020 (pdf of preprint)
  • Variational approach to rare event simulation using least-squares regression
    C. Hartmann, O. Kebiri, L. Neureither, L. Richter
    Chaos 29, 063107, 2019 (pdf of preprint)
  • Infinite-dimensional bilinear and stochastic balanced truncation
    S. Becker, C. Hartmann
    Math. Control Signals Systems 31(2), 1-37, 2019 (pdf of arXiv preprint)
  • Jarzysnki equality, fluctuation theorems and variance reduction: Mathematical analysis and numerical algorithms
    C. Hartmann, C. Schütte, W. Zhang
    J. Stat. Phys. 175(6), 1214–1261, 2019 (pdf of arXiv preprint)
  • Time scales and exponential trends to equilibrium: Gaussian model problems
    L. Neureither, C. Hartmann
    In: Giacomin G., Olla S., Saada E., Spohn H., Stoltz G. (eds) Stochastic Dynamics Out of Equilibrium. IHPStochDyn 2017. Springer Proceedings in Mathematics & Statistics, vol 282, pp. 391-410, Springer, Cham, 2019 (pdf of article)
  • Adaptive importance sampling with forward-backward stochastic differential equations
    O. Kebiri, L. Neureither, C. Hartmann
    In: Giacomin G., Olla S., Saada E., Spohn H., Stoltz G. (eds) Stochastic Dynamics Out of Equilibrium. IHPStochDyn 2017. Springer Proceedings in Mathematics & Statistics, vol 282, pp. 265-281, Springer, Cham, 2019 (pdf of article)
  • Balanced model reduction of linear systems with nonzero initial conditions: singular perturbation approximation
    A. Daraghmeh, C. Hartmann and N. Qatanani
    Appl. Math. Comput. 353, 295-307, 2019 (pdf of preprint)
  • Using agent-based modelling to simulate social-ecological systems across scales
    M. Lippe, M. Bithell, N. Gotts, D. Natalini, P. Barbrook-Johnson, C. Giupponi, M. Hallier, G. J. Hofstede, C. Le Page, R. B. Matthews, M. Schlüter,  P. Smith A. Teglio, K. Thellmann
    GeoInformatica 23(2), 269-298, 2019 (online first link)
  • Optimal control of linear systems with balanced reduced-order models: perturbation approximations
    A. Daraghmeh, C. Hartmann and N. Qatanani
    Appl. Math. Comput. 337, 119-136, 2018 (pdf of preprint)
  • Singularly perturbed forward-backward stochastic differential equations: application to the optimal control of bilinear systems
    O. Kebiri, L. Neureither, C. Hartmann
    Computation 6(3), 41, 2018 (pdf of article)
  • "How long will it take? Long, but not infinitely long." Modelling the long-term dynamics of stochastic evolutionary games
    M. Hallier, C. Hartmann
    Arne Ryde conference on Learning, Evolution and Games (LEG2018), 2018 (pdf of preprint)
  • Optimal control of Markov jump processes: Asymptotic analysis, algorithms, and application to modelling of chemical reaction systems
    W. Zhang, C. Hartmann, M. von Kleist,
    Commun. Math. Sci. 16(2), 293-331, 2018 (pdf of arXiv preprint)
  • WavePacket: A Matlab package for numerical quantum dynamics. II: Open quantum systems, optimal control, and model reduction
    B. Schmidt and C. Hartmann
    Comput. Phys. Commun. 228, 229-244, 2018 (pdf of preprint)
  • Importance sampling in path space for diffusion processes with slow-fast variables
    C. Hartmann, Ch. Schütte, M. Weber and W. Zhang,
    Probab. Theory Rel. Fields, 170(1-2), 177-228, 2018 (pdf file of preprint)
  • Variational characterization of free energy: theory and algorithms
    C. Hartmann, L. Richter, Ch. Schütte, W. Zhang
    Entropy 19, 626-653, 2017 (pdf of article)
  • Partitioning a macroscopic system into independent subsystems
    L. Delle Site, G. Ciccotti and C. Hartmann
    J. Stat. Mech. Theor. Exp., 2017(8), 083201, 2017 (ArXiv preprint)
  • Girsanov reweighting for path ensembles and Markov state models
    L. Donati, C. Hartmann and B.G. Keller
    J. Chem. Phys., 146, 244112, 2017 (ArXiv preprint)
  • Effective dynamics along given reaction coordinates, and reaction rate theory
    W. Zhang, C. Hartmann, Ch. Schütte,
    Farad. Discuss. 195, 365-394, 2016 (pdf file of preprint)
  • A sparse Markov chain approximation of LQ-type stochastic control problems
    R. Banisch and C. Hartmann,
    Math. Control Relat. F. 6, 363-389, 2016 (pdf file of preprint)
  • Model reduction algorithms for optimal control and importance sampling of diffusions
    C. Hartmann, Ch. Schütte, W. Zhang,
    Nonlinearity 29, 2298, 2016 (pdf file of preprint)
  • Constructing Markov State Models of Reduced Complexity from Agent-Based Simulation Data
    M. Hallier, C. Hartmann,
    Social Simulation Conference (SSC2016), 2016 (pdf file of preprint)
  • A Markov state modeling approach to characterizing the punctuated equilibrium dynamics of stochastic evolutionary games
    M. Hallier, C. Hartmann,
    GAMES 2016, 5th World Conference of the Game Theory Society, 2016 (pdf file of preprint)
  • Molecular dynamics in a Grand Ensemble: Bergmann-Lebowitz model and adaptive resolution simulation
    A. Agarwal, J. Zhu, H. Wang, C. Hartmann, L. Delle Site,
    New J. Phys. 17, 083042, 2015 (journal link)
  • Editorial: Scale bridging in molecular simulation
    C. Hartmann and L. Delle Site,
    Eur. Phys J. Special Topics 224, 2173-2176, 2015 (journal link)
  • Pseudo generators for under-resolved molecular dynamics
    A. Bittracher, C. Hartmann, O. Junge, P. Koltai,
    Eur. Phys J. Special Topics 224, 2463-2490, 2015 (pdf file of preprint)
  • Martingale-based gradient descent algorithm for estimating free energy values of diffusions
    H.C Lie, Ch. Schütte and C. Hartmann,
    Preprint, 2014 (pdf file of preprint)
  • Applications of the cross-entropy method to importance sampling and optimal control of diffusions
    W. Zhang, H. Wang, C. Hartmann, M. Weber and Ch. Schütte,
    SIAM J. Sci. Comput. 36, A2654-A2672, 2014 (pdf file of preprint)
  • Optimal control of multiscale systems using reduced-order models
    W. Zhang, J. Latorre, G. Pavliotis and C. Hartmann,
    J. Computational Dynamics 1, 279-306, 2014 (pdf file of preprint)
  • Meshless discretization of LQ-type stochastic control problems
    R. Banisch and C. Hartmann,
    arXiv:1309.7497, 2013 (pdf file of preprint)
  • The falling cat problem and shape effects in small molecules in a random environment: a case study
    C. Hartmann and T. Yanao,
    Mol. Phys. (Special Issue) 111, 3534-3545, 2013 (pdf file of preprint)
  • Linear response theory and optimal control for a molecular system under non-equilibrium conditions
    H. Wang, C. Hartmann and Ch. Schütte,
    Phys. (Special Issue) 111, 3555-3564, 2013 (pdf file of preprint)
  • Characterization of rare events in molecular dynamics
    C. Hartmann, R. Banisch, M. Sarich, T. Badowski and Ch. Schütte,
    Entropy 16, 350-376, 2013 (pdf file of preprint)
  • Markov state models for rare events in molecular dynamics
    M. Sarich, R. Banisch, C. Hartmann and Ch. Schütte
    Entropy 16, 258-286, 2013 (pdf file of preprint)
  • Balanced averaging of bilinear systems with applications to stochastic control
    C. Hartmann, B. Schäfer-Bung and A. Zueva
    SIAM J. Control Optim. 51, 2356-2378, 2013 (pdf file of preprint)
  • The reliability of the adaptive resolution technique in performing grand canonical-like molecular dynamics simulations
    H. Wang, C. Hartmann, L. Delle Site and Ch. Schütte
    Phys. Rev. X 3, 011018, 2013 (pdf file of preprint)
  • Efficient rare event simulation by optimal nonequilibrium forcing
    C. Hartmann and Ch. Schütte
    J. Stat. Mech. Theor. Exp. 2012, P11004, 2012 (pdf file of preprint)
  • Optimal control of molecular dynamics using Markov state models
    Ch. Schütte, S. Winkelmann, and C. Hartmann
    Math. Program. (Series B), 134, 259-282, 2012 (pdf file of preprint)
  • Variational collision integrator for polymer chains
    S. Leyendecker, C. Hartmann, M. Koch
    J. Comput. Phys. 231, 3896-3911, 2012 (pdf file of preprint)
  • Ambient space formulations and statistical mechanics of holonomically constrained Langevin systems
    J. Walter, C. Hartmann, and J. Maddocks
    Eur. Phys. J. Special Topics 200, 153-181, 2011 (pdf file of preprint)
  • On two possible definitions of the free energy for collective variables
    C. Hartmann, J. Latorre and G. Ciccotti
    Eur. Phys. J. Special Topics 200, 73-89, 2011 (pdf file of preprint)
  • Dimension reduction by balanced truncation: Application to light-induced control of open quantum systems
    B. Schäfer-Bung, C. Hartmann, B. Schmidt and Ch. Schütte
    J. Chem. Phys. 135, 014112, 2011 (pdf file of preprint)
  • A Structure-preserving numerical discretization of reversible diffusions
    J. Latorre, Ph. Metzner, C. Hartmann and Ch. Schütte
    Commun. Math. Sci. 9, 1051-1072, 2011 (pdf file of preprint)
  • Balanced model reduction of partially-observed Langevin equations: an averaging principle
    C. Hartmann
    Math. Comput. Model. Dyn. Syst. 17, 463-490, 2011 (pdf file of preprint)
  • Free energy computation by controlled Langevin processes
    J. Latorre, C. Hartmann, Ch. Schütte
    Procedia Computer Science 1, pp. 1591-1600, 2010 (pdf file of preprint)
  • On the linear response of mechanical systems with constraints
    C. Hartmann, Ch. Schütte and G. Ciccotti
    J. Chem. Phys. 132, 111103, 2010 (pdf file of preprint)
  • Balanced truncation of linear second-order systems: A Hamiltonian approach
    C. Hartmann, V.-M. Vulcanov, Ch. Schütte
    Multiscale Model. Simul. 8, No. 4, pp. 1348 - 1367, 2010 (pdf file of preprint)
  • Balancing of dissipative Hamiltonian systems
    C. Hartmann
    In: Proceedings of MATHMOD 09, I.Troch and F. Breitenecker (eds.), ARGESIM Report 35, pp. 1244-1255, 2009 (pdf file of preprint)
  • Fast simulation of polymer chains
    C. Hartmann, Ch. Schütte, G.Kalibaeva, M. di Pierro, G. Ciccotti
    J. Chem. Phys. 130, 144101, 2009 (pdf file of reprint)
  • Conformation Dynamics
    Ch. Schütte, F. Noe, E. Meerbach, Ph. Metzner, C. Hartmann
    In: Proceedings of the 6th International Congress on Industrial and Applied Mathematics, I. Jeltsch and G. Wanner (eds.), pp. 297-335, 2009 (pdf file of preprint)
  • Balancing of partially-observed stochastic differential equations
    C. Hartmann, Ch. Schütte
    47th IEEE Conference on Decision and Control, pp. 4867-4872, 2008 (pdf file of reprint)
  • An ergodic sampling scheme for constrained Hamiltonian systems with applications to molecular dynamics
    C. Hartmann
    J. Stat. Phys. 130, No. 4, pp. 687-712, 2008 (pdf file of preprint)
  • Data-based parameter estimation of generalized multidimensional Langevin processes
    I. Horenko, F. Noe, C. Hartmann, Ch. Schütte
    Phys. Rev. E 76, 016706, 2007 (pdf file of reprint)
  • Comment on two distinct notions of free energy
    C. Hartmann, Ch. Schütte
    Physica D 228, No. 1, pp. 59-63, 2007 (pdf file of preprint)
  • A constrained hybrid Monte-Carlo algorithm and the problem of calculating the free energy in several variables
    C. Hartmann, Ch. Schütte
    Z. Angew. Math. Mech. 85, No. 10, pp. 700-710, 2005 (pdf file of preprint)
  • A geometric approach to constrained molecular dynamics and free energy
    C. Hartmann, Ch. Schütte
    Commun. Math. Sci. 3, No. 1, pp 1-20, 2005 (pdf file of reprint)
  • An averaging principle for fast degrees of freedom exhibiting long-term correlations
    Ch. Schütte, J. Walter, C. Hartmann, W. Huisinga
    Multiscale Model. Simul. 2, No. 3, pp. 501-526, 2004 (pdf file of reprint)