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)

PDF
747kB |

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

## Abstract

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 |
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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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