Repository: Freie Universität Berlin, Math Department

Optimal Reaction Coordinates: Variational Characterization and Sparse Computation

Bittracher, Andreas and Mollenhauer, Mattes and Koltai, Péter and Schütte, Ch. (2023) Optimal Reaction Coordinates: Variational Characterization and Sparse Computation. Multiscale Modeling & Simulation, 21 (2). ISSN ISSN (print): 1540-3459 ISSN (online): 1540-3467

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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.

Item Type:Article
Uncontrolled Keywords:reaction coordinates coarse graining variational principle machine learning sparsity
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Deterministic and Stochastic PDEs Group
ID Code:3096
Deposited By: Ulrike Eickers
Deposited On:19 Feb 2024 14:04
Last Modified:19 Feb 2024 14:04

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