Abstract of the talk// Metastable molecular dynamics exhibit long dwelling times in a few dominant regions and rare transitions that govern long-term behavior. Transfer-operator viewpoints provide a principled way to characterize these slow processes through dominant eigenvalues and eigenfunctions, yielding reduced kinetic descriptions such as Markov state models and variational/Koopman-inspired approaches.

A central challenge is to identify low-dimensional collective variables (CVs) that are dynamically informative, i.e., retain the essential slow modes and enable quantitatively reliable effective dynamics on latent space. Building on Koopman-operator structure, the talk focuses on how dominant invariant subspaces can be learned from simulation data (e.g., via ISOKANN-style neural subspace learning), how this yields effective generators/dynamics in CV space, and how these reduced models connect to transition rates, committors, and pathways.

Even with an accurate effective model, practical use in rare-event settings hinges on lifting: converting a coarse CV trajectory into dynamically consistent full-dimensional states and transition-path ensembles. An on-the-fly lifting strategy is presented that uses a cheap coarse reference path to guide full-system trajectories, and then corrects the induced bias via pathwise Girsanov reweighting, producing a correct-by-construction importance-sampling approximation of the uncontrolled dynamics conditioned on the coarse information. The talk also highlights the link to stochastic optimal control as a framework for designing variance-reducing guidance.