Overview Statistic: PDF-Downloads (blue) and Frontdoor-Views (gray)

Optimal Reaction Coordinates: Variational Characterization and Sparse Computation

  • 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.

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics - number of accesses to the document
Author:Andreas Bittracher, Mattes Mollenhauer, Péter Koltai, Christof Schütte
Document Type:Article
Parent Title (English):Multiscale Modelling & Simulation
First Page:449
Last Page:488
Year of first publication:2023
ArXiv Id:http://arxiv.org/abs/2107.10158
Accept ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.