ArticleJournal of nonlinear science2018
Transition Manifolds of Complex Metastable Systems: Theory and Data-Driven Computation of Effective Dynamics.
Article in Journal of nonlinear science, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
What it found
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
10 citing papers in PubMed.
- Random Functions as Data Compressors for Machine Learning of Molecular Processes.Journal of chemical theory and computation · 2026Article
- Random walk based snapshot clustering for detecting community dynamics in temporal networks.Scientific reports · 2025Article
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- Fluctuating landscapes and heavy tails in animal behavior.bioRxiv : the preprint server for biology · 2023Article
- Collective variable discovery in the age of machine learning: reality, hype and everything in between.RSC advances · 2022Review
- A Small Molecule Stabilizes the Disordered Native State of the Alzheimer's Aβ Peptide.ACS chemical neuroscience · 2022Article
- TYROSINE KINASES: COMPLEX MOLECULAR SYSTEMS CHALLENGING COMPUTATIONAL METHODOLOGIES.The European physical journal. B · 2021Article
- Molecular latent space simulators.Chemical science · 2020Article
- Galerkin approximation of dynamical quantities using trajectory data.The Journal of chemical physics · 2019Article
- Article
Corrections and comments
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Authors and funding
6 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.