TY - JOUR A1 - Witzig, Jakob A1 - Beckenbach, Isabel A1 - Eifler, Leon A1 - Fackeldey, Konstantin A1 - Gleixner, Ambros A1 - Grever, Andreas A1 - Weber, Marcus T1 - Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes JF - Multiscale Modeling and Simulation N2 - In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst. KW - Markov State Models KW - NESS KW - Non-reversible Markov Processes KW - Mixed-Integer Programming Y1 - 2018 U6 - https://doi.org/10.1137/16M1091162 SN - 1438-0064 VL - 16 IS - 1 SP - 248 EP - 265 ER - TY - JOUR A1 - Donati, Luca A1 - Schütte, Christof A1 - Weber, Marcus T1 - The Kramers turnover in terms of a macro-state projection on phase space JF - Molecular Physics N2 - 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. Y1 - 2025 U6 - https://doi.org/10.1080/00268976.2024.2356748 VL - 123 IS - 7-8: Giovanni Ciccotti: A Renaissance Physicist SP - e2356748 PB - Taylor & Francis 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 -