@article{ZhangSchuette2023, author = {Zhang, Wei and Sch{\"u}tte, Christof}, title = {Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics}, volume = {23}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {4}, doi = {10.1002/pamm.202300189}, year = {2023}, abstract = {High-dimensional metastable molecular dynamics (MD) can often be characterised by a few features of the system, that is, collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning-based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning-based approaches for finding CVs, either by computing leading eigenfunctions of transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples.}, language = {en} } @misc{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}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65045}, year = {2017}, abstract = {The article surveys and extends variational formulations of the thermodynamic free energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations. The implications of the different variational formulations for designing efficient stochastic optimization and nonequilibrium simulation algorithms for computing free energies are discussed and illustrated.}, language = {en} } @article{DonatiSchuetteWeber2025, author = {Donati, Luca and Sch{\"u}tte, Christof and Weber, Marcus}, title = {The Kramers turnover in terms of a macro-state projection on phase space}, volume = {123}, journal = {Molecular Physics}, number = {7-8: Giovanni Ciccotti: A Renaissance Physicist}, publisher = {Taylor \& Francis}, doi = {10.1080/00268976.2024.2356748}, pages = {e2356748}, year = {2025}, abstract = {We have investigated how Langevin dynamics is affected by the friction coefficient using the novel algorithm ISOKANN, which combines the transfer operator approach with modern machine learning techniques. ISOKANN describes the dynamics in terms of an invariant subspace projection of the Koopman operator defined in the entire state space, avoiding approximations due to dimensionality reduction and discretization. Our results are consistent with the Kramers turnover and show that in the low and moderate friction regimes, metastable macro-states and transition rates are defined in phase space, not only in position space.}, language = {en} } @inproceedings{SunkaraRostamivonTycowiczetal.2026, author = {Sunkara, Vikram and Rostami, Atefe and von Tycowicz, Christoph and Sch{\"u}tte, Christof}, title = {Stop throwing away your Decoder; extract the learnt local coordinate system using Latent-XAI}, booktitle = {The 4th World Conference on Explainable Artificial Intelligence (XAI-2026)}, year = {2026}, language = {en} } @article{WehlitzPavliotisSchuetteetal.2026, author = {Wehlitz, Nathalie and Pavliotis, Grigorios and Sch{\"u}tte, Christof and Winkelmann, Stefanie}, title = {Data-driven Reduction of Transfer Operators for Particle Clustering Dynamics}, arxiv = {http://arxiv.org/abs/2601.02932}, year = {2026}, abstract = {We develop an operator-based framework to coarse-grain interacting particle systems that exhibit clustering dynamics. Starting from the particle-based transfer operator, we first construct a sequence of reduced representations: the operator is projected onto concentrations and then further reduced by representing the concentration dynamics on a geometric low-dimensional manifold and an adapted finite-state discretization. The resulting coarse-grained transfer operator is finally estimated from dynamical simulation data by inferring the transition probabilities between the Markov states. Applied to systems with multichromatic and Morse interaction potentials, the reduced model reproduces key features of the clustering process, including transitions between cluster configurations and the emergence of metastable states. Spectral analysis and transition-path analysis of the estimated operator reveal implied time scales and dominant transition pathways, providing an interpretable and efficient description of particle-clustering dynamics.}, language = {en} } @article{SchuetteSikorskiKresseetal.2026, author = {Sch{\"u}tte, Christof and Sikorski, Alexander and Kresse, Jakob and Weber, Marcus}, title = {On-the-Fly Lifting of Coarse Reaction-Coordinate Paths to Full-Dimensional Transition Path Ensembles}, arxiv = {http://arxiv.org/abs/2603.23266}, doi = {10.48550/arXiv.2603.23266}, year = {2026}, abstract = {Effective dynamics on a low-dimensional collective-variable (CV) or latent space can be simulated far more cheaply than the underlying high-dimensional stochastic system, but exploiting such coarse predictions requires lifting: turning a coarse CV trajectory into dynamically consistent full-dimensional states and path ensembles, without relying on global sampling of invariant or conditional fiber measures. We present a local, on-the-fly lifting strategy based on guided full-system trajectories. First an effective model in CV space is used to obtain a coarse reference trajectory. Then, an ensemble of full-dimensional trajectories is generated from a guided version of the original dynamics, where the guidance steers the trajectory to track the CV reference path. Because guidance biases the path distribution, we correct it via pathwise Girsanov reweighting, yielding a correct-by-construction importance-sampling approximation of the conditional law of the uncontrolled dynamics. We further connect the approach to stochastic optimal control, clarifying how coarse models can inform variance-reducing guidance for rare-event quantities. Numerical experiments demonstrate that inexpensive coarse transition paths can be converted into realistic full-system transition pathways (including barrier crossings and detours) and can accelerate estimation of transition pathways and statistics while providing minimal bias through weighted ensembles.}, language = {en} }