Summary: In stochastic systems, multiple long-lived states might coexists, in which the system spends a large amount of time before spontaneously and often catastrophically switching to a different long-lived state. For example, in molecular dynamics, the reactant and the product state both correspond to local minima in an energy landscape, but thermal activation pushed the system across the separating energy barrier, corresponding to the chemical reaction. Similarly, Earth's climate might spend a long time in a certain long-lived state, but climate change might push it across a tipping point, such that the state of the climate abruptly changes. Often, these changes are hard to predict and rare on the intrinsic time scale of the system. In this project, algorithms are developed to simulate only those trajectories of the stochastic system that exhibit the transition. This transition path sampling or bridge sampling allows to generate for example conditional statistics, analyze physical causes responsible for the transition, or even develop early warning signs for an anticipated transition in progress.
Relevant publications
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T. Grafke, "Sampling conditioned diffusions via Pathspace Projected Monte Carlo", ArXiv (2025) (link)
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T. Grafke, A. Laio, "Metadynamics for transition paths in irreversible dynamics", Multiscale Modeling & Simulation, Vol. 22, Iss. 1 (2024) (link)