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Transition Path Sampling Using Koopman Operators and Exit-Time Optimal Control — arXiv:2610.10054

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.10054
License (as archived): CC0-1.0
Archived: 2026-10-08T12:37:19.301Z
SHA-256 of the archived text: 257ccc9c71b51fc2a2246cba14087d3bb33f09b86dc115ebce14469a3bd0e2e2
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How to cite

Transition Path Sampling Using Koopman Operators and Exit-Time Optimal Control — arXiv:2610.10054 — arXiv (en), https://arxiv.org/abs/2610.10054 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2ed79fdaf03d (Metraipolis archive dc_2ed79fdaf03d, sha256 257ccc9c71b51fc2a2246cba14087d3bb33f09b86dc115ebce14469a3bd0e2e2)

BibTeX

@misc{dc2ed79fdaf03d,
  title = {Transition Path Sampling Using Koopman Operators and Exit-Time Optimal Control — arXiv:2610.10054},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.10054},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2ed79fdaf03d; sha256 257ccc9c71b51fc2a2246cba14087d3bb33f09b86dc115ebce14469a3bd0e2e2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.10054. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Sampling transitions between metastable states is a central problem in dynamical systems theory and molecular dynamics in particular. A key challenge is the existence of high free-energy barriers that separate the states, making transitions extremely rare. Recent machine learning-based methods cast transition path sampling (TPS) as an optimal stochastic control (OSC) problem over a fixed time horizon, and parameterize the drift bias via a neural network trained by simulation-in-the-loop, requiring repeated biased rollouts. To address computational and performance guarantee issues of these models, we propose a new approach for the problem based on Koopman operators. Because Koopman operators are linear, their leading eigenfunctions reveal the metastable sets and provide an estimate of the committor function with no transition path information required. Furthermore, we formulate TPS as an OSC problem up to an exit time. Our time horizon is the first hitting time of the target set, and our running cost penalizes time spent in nonreactive regions by encoding the estimated committor function. We derive the optimal controller in closed form and approximate it in a reproducing kernel Hilbert space (RKHS). This reduces the problem of constructing the optimal controller to solving a single equality-constrained quadratic program, whose solution can be characterized by a linear Karush-Kuhn-Tucker (KKT) system. On the two-channel double well and alanine dipeptide, our controller increases the fraction of trajectories reaching the target from 0% to 99.8% within 1000 steps, and from 0% to 93% within 1ps, respectively.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Systems and Control (eess.SY) ; Machine Learning (cs.LG); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2610.10054 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T12:14:15.439Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).