TY - JOUR A1 - Hartmann, Carsten A1 - Jöster, Annika A1 - Schütte, Christof A1 - Sikorski, Alexander A1 - Weber, Marcus T1 - Importance sampling of unbounded random stopping times: computing committor functions and exit rates without reweighting N2 - Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on average exponentially long compared to the characteristic timescale of the system, with waiting time distributions that have (sub)exponential tails and infinite support. As a result, sampling such rare events can lead to trajectories that can be become arbitrarily long, with not too low probability, which makes the reweighting of such trajectories a real challenge. Here, we discuss rare event simulation by importance sampling from a variational perspective, with a focus on applications in molecular dynamics, in particular the computation of committor functions. The idea is to design importance sampling schemes that (a) reduce the variance of a rare event estimator while controlling the average length of the trajectories and (b) that do not require the reweighting of possibly very long trajectories. In doing so, we study different stochastic control formulations for committor and mean first exit times, which we compare both from a theoretical and a computational point of view, including numerical studies of some benchmark examples. Y1 - 2026 ER - TY - CHAP A1 - Yousefian, Maryam A1 - Donati, Luca A1 - Sikorski, Alexander A1 - Weber, Marcus A1 - Röblitz, Susanna T1 - Exploring Metastable Dynamics of Gene Regulatory Networks with ISOKANN T2 - Computational Methods in Systems Biology. CMSB 2025 N2 - Stochastic dynamical systems like gene regulatory networks (GRNs) often exhibit behavior characterized by metastable sets (representing cellular phenotypes), in which trajectories remain for long times, whereas switches between these sets in the phase space are rare events. One way to capture these rare events is to infer the system’s long-term behavior from the spectral characteristics (eigenvalues and eigenvectors) of its Koopman operator. For GRNs, the Koopman operator is based on the chemical master equation (CME), which provides a precise mathematical modeling framework for stochastic GRNs. Since the CME is typically analytically intractable, methods based on discretizing the CME operator have been developed. However, determining the number and location of metastable sets in the phase space as well as the transition rates between them remains computationally challenging, especially for large GRNs with many genes and interactions. A promising alternative method, called ISOKANN (invariant subspaces of Koopman operators with artificial neural networks) has been developed in the context of molecular dynamics. ISOKANN uses a combination of the power iteration and neural networks to learn the basis functions of an invariant subspace of the Koopman operator. In this paper, we extend the application of ISOKANN to the CME operator and apply it to two small GRNs: a genetic toggle switch model and a model for macrophage polarization. Our work opens a new field of application for the ISOKANN algorithm and demonstrates the potential of this algorithm for studying large GRNs. Y1 - 2026 U6 - https://doi.org/10.1007/978-3-032-01436-8_8 VL - 15959 SP - 126 EP - 149 ER - TY - JOUR A1 - Kresse, Jakob A1 - Sikorski, Alexander A1 - Chewle, Surahit A1 - Sunkara, Vikram A1 - Weber, Marcus T1 - Revealing the Atomistic Mechanism of Rare Events in Molecular Dynamics JF - Journal of Chemical Theory and Computation N2 - Interpretable reaction coordinates are essential for understanding rare conformational transitions in molecular dynamics. The Atomistic Mechanism Of Rare Events in Molecular Dynamics (AMORE-MD) framework enhances interpretability of deep-learned reaction coordinates by connecting them to atomistic mechanisms, without requiring any a priori knowledge of collective variables, pathways, or endpoints. Here, AMORE-MD employs the ISOKANN algorithm to learn a neural membership function χ representing the dominant slow process, from which transition pathways are reconstructed as minimum-energy paths aligned with the gradient of χ, and atomic contributions are quantified through gradient-based sensitivity analysis. Iterative enhanced sampling further enriches transition regions and improves coverage of rare events enabling recovery of known mechanisms and chemically interpretable structural rearrangements at atomic resolution for the Müller-Brown potential, alanine dipeptide, and the elastin-derived hexapeptide VGVAPG. Y1 - 2026 U6 - https://doi.org/10.1021/acs.jctc.5c01906 VL - 22 IS - 5 SP - 2380 EP - 2389 ER - TY - JOUR A1 - Schütte, Christof A1 - Sikorski, Alexander A1 - Kresse, Jakob A1 - Weber, Marcus T1 - On-the-Fly Lifting of Coarse Reaction-Coordinate Paths to Full-Dimensional Transition Path Ensembles N2 - 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. Y1 - 2026 U6 - https://doi.org/10.48550/arXiv.2603.23266 ER -