Repository: Freie Universität Berlin, Math Department

Variational Characterization and Identification of Reaction Coordinates in Stochastic Systems

Bittracher, Andreas and Mollenhauer, Mattes and Koltai, Péter and Schütte, Christof (2021) Variational Characterization and Identification of Reaction Coordinates in Stochastic Systems. arXive . pp. 1-33. (Unpublished)

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Official URL: https://arxiv.org/abs/2107.10158

Abstract

Reaction coordinates are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic systems. We present a novel, very general characterization of these coordinates and provide conditions for their existence. We show that these conditions are ful�lled for slow-fast systems, metastable systems, and other systems with known good reaction coordinates. Further, we formulate these conditions as a variational principle, i.e., de�ne a loss function whose minimizers are optimal reaction coordinates. Remarkably, the numerical e�ort required to evaluate the loss function scales only with the complexity of the underlying, low-dimensional mechanism, and not with that of the full system. In summary, we provide the theoretical foundation for an e�cient computation of reaction coordinates via modern machine learning techniques.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:2603
Deposited By: Monika Drueck
Deposited On:17 Sep 2021 12:19
Last Modified:25 Oct 2021 20:28

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