Repository: Freie Universität Berlin, Math Department

Optimal Reaction Coordinates: Variational Characterization and Sparse Computation

Bittracher, Andreas and Mollenhauer, Mattes and Koltai, Péter and Schütte, Christof (2021) Optimal Reaction Coordinates: Variational Characterization and Sparse Computation. ArXiv . pp. 1-36. (Submitted)

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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 very good approximation of the long-term dynamics of the original highdimensional process. We show that, for slow-fast systems, metastable systems, and other systems with known good RCs, the novel theory reproduces previous insight. 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. The theory provided lays the foundation for an e�cient and data-sparse computation of RCs 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
ID Code:2612
Deposited By: Monika Drueck
Deposited On:24 Sep 2021 11:06
Last Modified:24 Sep 2021 11:06

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