## Title data

Bittracher, Andreas ; Mollenhauer, Mattes ; Koltai, Peter ; Schütte, Christof:

**Optimal reaction coordinates : Variational characterization and sparse computation.**

*In:* Multiscale Modeling & Simulation.
Vol. 21
(2023)
Issue 2
.
- pp. 449-488.

ISSN 1540-3467

DOI: https://doi.org/10.1137/21M1448367

## Abstract in another language

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.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | reaction coordinates; coarse graining; variational principle; machine learning; sparsity |

Subject classification: | MSC Codes: 60G25, 60J25, 65K10, 62D99 |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Dynamical Systems and Data > Chair Dynamical Systems and Data - Univ.-Prof. Dr. Peter Koltai Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Dynamical Systems and Data |

Result of work at the UBT: | No |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 11 Jan 2023 13:03 |

Last Modified: | 23 May 2023 05:27 |

URI: | https://eref.uni-bayreuth.de/id/eprint/73283 |