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Bittracher, Andreas ; Mollenhauer, Mattes ; Koltai, Peter ; Schütte, Christof:
Optimal reaction coordinates : Variational characterization and sparse computation.
In: Multiscale Modeling & Simulation.
Bd. 21
(2023)
Heft 2
.
- S. 449-488.
ISSN 1540-3467
DOI: https://doi.org/10.1137/21M1448367
Abstract
Reaction coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and general variational characterization of optimal RCs and provide conditions for their existence. Optimal RCs are minimizers of a certain loss function, and reduced models based on them guarantee a good approximation of the statistical long-term properties of the original high-dimensional process. We show that for slow-fast systems, metastable systems, and other systems with known good RCs, the novel theory reproduces previous insight. Remarkably, for reversible systems, the numerical effort required to evaluate the loss function scales only with the variability of the underlying, low-dimensional mechanism, and not with that of the full system. The theory provided lays the foundation for an efficient and data-sparse computation of RCs via modern machine learning techniques.
Weitere Angaben
| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Keywords: | reaction coordinates; coarse graining; variational principle; machine learning; sparsity |
| Fachklassifikationen: | MSC Codes: 60G25, 60J25, 65K10, 62D99 |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Dynamical Systems and Data > Lehrstuhl Dynamical Systems and Data - Univ.-Prof. Dr. Peter Koltai Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Dynamical Systems and Data |
| Titel an der UBT entstanden: | Nein |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 11 Jan 2023 13:03 |
| Letzte Änderung: | 23 Mai 2023 05:27 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/73283 |