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Article

Delle Site, Luigi and Hartmann, Carsten (2024) Computationally feasible bounds for the free energy of nonequilibrium steady states, applied to simple models of heat conduction. Molecular Physics .

Sun, Jingtong and Berner, Julius and Richter, Lorenz and Zeinhofer, Marius and Müller, Johannes and Azizzadenesheli, Kamyar and Anandkumar, Anima (2024) Dynamical Measure Transport and Neural PDE Solvers for Sampling. Preprint arXiv . (Unpublished)

Winkler, Ludwig and Richter, Lorenz and Opper, Manfred (2024) Bridging discrete and continuous state spaces: Exploring the Ehrenfest process in time-continuous diffusion models. Preprint arXiv . (Unpublished)

Berner, Julius and Richter, Lorenz and Ullrich, Karen (2024) An optimal control perspective on diffusion-based generative modeling. Preprint arXiv . (Unpublished)

Quer, Jannes and Ribera Borrell, Enric (2024) Connecting Stochastic Optimal Control and Reinforcement Learning. Submitted Preprint . (Submitted)

Hartmann, Carsten and Jöster, Annika (2024) Risk-neutral limit of adaptive importance sampling of random stopping times. Submitted to 26th International Symposium on Mathematical Theory of Networks and Systems . (Submitted)

Delle Site, Luigi and Hartmann, Carsten (2024) Scaling law for the size dependence of a short-ranged quantum gas. Physical Review A, 109 .

Delle Site, Luigi and Hartmann, Carsten (2024) Scaling law for the size dependence of a finite-range quantum gas. Physical Review A, 109 (2).

Sikorski, Alexander and Ribera Borrell, Enric and Weber, Marcus (2024) Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN. Journal of Mathematical Physics, 65 (1).

Borrell, Enric Ribera and Quer, Jannes and Richter, Lorenz and Schütte, Christof (2023) Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics. Preprint to appear in SISC 2024 . (In Press)

Richter, Lorenz and Sallandt, Leon and Nüsken, Nikolas (2023) From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs. Preprint . (Unpublished)

Richter, Lorenz and Berner, Julius and Liu, Guang-Horng (2023) Improved sampling via learned diffusions. Preprint . (Unpublished)

Reible, Benedikt M. and Hille, Julian F. and Hartmann, Carsten and Delle Site, Luigi (2023) Finite-size effects and thermodynamic accuracy in many-particle systems. Physical Review Research, 5 (2).

Schütte, Christof and Klus, Stefan and Hartmann, Carsten (2023) Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning. Acta Numerica, 32 . pp. 517-673.

Nüsken, Nikolas and Richter, Lorenz (2023) Interpolating Between BSDEs and PINNs: Deep Learning for Elliptic and Parabolic Boundary Value Problems. Journal of Machine Learning, 2 . pp. 31-64.

Reible, Benedikt and Hartmann, Carsten and Delle Site, Luigi (2022) Two-sided Bogoliubov inequality to estimate finite size effects in quantum molecular simulations. Letters in Mathematical Physics, 112 (97).

Richter, Lorenz and Berner, Julius (2022) Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning. Preprint arXiv . (Unpublished)

Becker, Simon and Hartmann, Carsten and Redmann, Martin and Richter, Lorenz (2022) Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces. Stochastic Processes and their Applications, 149 . pp. 107-141.

Breiten, T. and Hartmann, Carsten and Neureither, Lara and Sharma, Upanshu (2021) Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: a stochastic control approach. Journal of Mathematical Physics, 62 (12). pp. 1-19.

Hartmann, Carsten and Neureither, Lara and Stehlau, Markus (2021) Reachability Analysis of Randomly Perturbed Hamiltonian Systems. IFAC-PapersOnLine, 54 (19). pp. 307-3014.

Nüsken, Nikolas and Richter, Lorenz (2021) Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space. Partial Differential Equations and Applications, 2 (48). pp. 1-48.

Sikorski, Alexander and Weber, Marcus and Schütte, Christof (2021) The augmented jump chain – a sparse representationof time-dependent Markov jump processes. Advanced Theory and Simulations, 4(4):2000274, 2021, 4 (4).

Richter, Lorenz and Sallandt, Leon and Nüsken, Nikolas (2021) Solving high-dimensional parabolic PDEs using the tensor train format. Proceedings of the 38th International Conferenceon Machine Learning, 139 . pp. 8998-9009.

Hartmann, C. and Richter, L. (2021) Nonasymptotic bounds for suboptimal importance sampling. To appear 2024 in SIAM/ASA Journal on Uncertainty Quantification . (In Press)

Bouanani, Hafida and Hartmann, Carsten and Kebiri, Omar (2021) Model reduction and uncertainty quantification of multiscale diffusions with parameter uncertainties using nonlinear expectations. arXive . pp. 1-22. (Submitted)

Sechi, Renata and Sikorski, Alexander and Weber, Marcus (2021) Estimation of the Koopman generator by Newton’s extrapolation. SIAM Multiscale Modeling & Simulation, 19 (2). pp. 758-774. ISSN print: 1540-3459; online: 1540-3467

Richter, Lorenz and Boustati, Ayman and Nüsken, Nikolas and Ruiz, Francisco J. R. and Akyildiz, Ömer Deniz (2020) VarGrad: A Low-Variance Gradient Estimator for Variational Inference. Advances in Neural Information Processing Systems 2020 . pp. 1-25. (Submitted)

Helfmann, Luzie and Ribera Borrell, Enric and Schütte, Christof and Koltai, Péter (2020) Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics. Journal of Nonlinear Science, 30 . pp. 3321-3366.

Becker, Simon and Richter, Lorenz (2020) Model order reduction for (stochastic-) delay equations with error bounds. arXive . pp. 1-23. (Submitted)

Nüsken, N. and Richter, L. (2020) Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space. SFB 1114 Preprint in arXiv . pp. 1-40. (Submitted)

Hartmann, C. and Neureither, L. and Sharma, U. (2020) Coarse-graining of non-reversible stochastic differential equations: quantitative results and connections to averaging. SIAM Journal on Mathematical Analysis, 52 (3). pp. 2689-2733.

Ray, Sourav and Sunkara, Vikram and Schütte, Christof and Weber, Marcus (2020) How to calculate pH-dependent binding rates for receptor–ligand systems based on thermodynamic simulations with different binding motifs. Molecular Simulation, 46 (18). pp. 1443-1452.

Becker, Simon and Hartmann, Carsten and Redmann, Martin and Richter, Lorenz (2019) Feedback control theory & Model order reduction for stochastic equations. ArXive . pp. 1-36. (Submitted)

Hartmann, Carsten and Kebiri, Omar and Neureither, Lara and Richter, Lorenz (2019) Variational approach to rare event simulation using least-squares regression. Chaos, 29 (6). ISSN 1054-1500 (print); 1089-7682 (online)

Hartmann, C. and Schütte, Ch. and Zhang, W. (2019) Jarzysnki equality, fluctuation theorems and variance reduction: Mathematical analysis and numerical algorithms. J. Stat. Phys., 175 (6). pp. 1214-1261. ISSN 0022-4715; ESSN: 1572-9613

Donati, L. and Heida, M. and Weber, M. and Keller, B. (2018) Estimation of the infinitesimal generator by square-root approximation. Journal of Physics: Condensed Matter, 30 (42). p. 425201. ISSN 0953-8984, ESSN: 1361-648X

Kebiri, O. and Neureither, L. and Hartmann, C. (2018) Singularly perturbed forward-backward stochastic differential equations: application to the optimal control of bilinear systems. Computation, 6 (3). p. 41. ISSN 2079-3197 (online)

Hartmann, C. and Schütte, Ch. and Weber, M. and Zhang, W. (2018) Importance sampling in path space for diffusion processes with slow-fast variables. Probab. Theory Rel. Fields, 170 (1-2). pp. 177-228. ISSN 0178-8051 (print) 1432-2064 (online)

Weber, M. (2018) Implications of PCCA+ in Molecular Simulation. Computation, 6 (1). ISSN 2079-3197 (online)

Hartmann, C. and Richter, L. and Schütte, Ch. and Zhang, W. (2017) Variational characterization of free energy: theory and algorithms. Entropy (Special Issue), 19 (11). pp. 1-27. ISSN 1099-4300

Quer, J. and Lie, H. (2017) Some connections between importance sampling and enhanced sampling methods in molecular dynamics. Journal of Chemical Physics . pp. 1-19. ISSN 0021-9606

Delle Site, L. and Ciccotti, G. and Hartmann, C. (2017) Partitioning a macroscopic system into independent subsystems. Journal of Statistical Mechanics: Theory and Experiment, 2017 . pp. 1-13.

Quer, J. and Donati, L. and Keller, B.G. and Weber, M. (2017) An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates. SIAM J. Sci. Comput. . pp. 1-19. ISSN 1064-8275 (print) (In Press)

Weber, M. and Fackeldey, K. and Schütte, Ch. (2017) Set-free Markov state model building. Journal of Chemical Physics, 146 (12). p. 124133.

Koltai, P. and Ciccotti, G. and Schütte, Ch. (2016) On metastability and Markov state models for non-stationary molecular dynamics. Journal of Chemical Physics, 145 (17). p. 174103.

Quer, J. and Weber, M. (2016) Estimating exit rate for rare event dynamical systems by extrapolation. ZIB-Report . pp. 1-19. ISSN 2192-7782 (online)

Banisch, Ralf and Hartmann, C. (2016) A sparse Markov chain approximation of LQ-type stochastic control problems. Math. Control Relat. F., 6 (3). pp. 363-389. ISSN 1064-8275

Hartmann, C. and Schütte, Ch. and Zhang, W. (2016) Model reduction algorithms for optimal control and importance sampling of diffusions. Nonlinearity, 29 (8). pp. 2298-2326. ISSN 0951-7715

Zhang, W. and Hartmann, C. and Schütte, Ch. (2016) Effective dynamics along given reaction coordinates, and reaction rate theory. Faraday discussions, 195 . pp. 365-394. ISSN 1359-6640

Bittracher, Andreas and Hartmann, C. and Junge, O. and Koltai, Péter (2015) Pseudo generators for under-resolved molecular dynamics. The European Physical Journal Special Topics, 224 (12). pp. 2463-2490. ISSN 1951-6355

Hartmann, C. and Latorre, J.C. and Pavliotis, G. A. and Zhang, W. (2014) Optimal control of multiscale systems using reduced-order models. J. Computational Dynamics, 1 (2). pp. 279-306. ISSN 2158-2505

Lie, Han Cheng and Schütte, Ch. and Hartmann, C. (2014) Martingale-based gradient descent algorithm for estimating free energy values of diffusions. SIAM J. Sci. Comput. . ISSN 1064-8275 (Submitted)

Book Section

Kebiri, Omar and Neureither, Lara and Hartmann, Carsten (2019) Adaptive importance sampling with forward-backward stochastic differential equations. In: Stochastic Dynamics Out of Equilibrium. Springer Proceedings in Mathematics & Statistics, 282 . Springer International Publishing, pp. 265-281. ISBN 978-3-030-15095-2

Neureither, L. and Hartmann, C. (2019) Time scales and exponential trends to equilibrium: Gaussian model problems. In: Stochastic Dynamics Out of Equilibrium. IHPStochDyn 2017. Springer Proceedings in Mathematics & Statistics, 282 . Springer, pp. 391-410. ISBN 978-3-030-15095-2