Data-driven approximation of the Koopman generator: Model reduction, system identification, and control

被引：184

作者：

Klus, Stefan ^{[1
]}

Nuske, Feliks ^{[2
,3
,4
]}

Peitz, Sebastian ^{[4
]}

Niemann, Jan-Hendrik ^{[5
]}

Clementi, Cecilia ^{[2
,3
]}

Schuette, Christof ^{[1
,5
]}

机构：

[1] Free Univ Berlin, Dept Math & Comp Sci, Berlin, Germany

[2] Rice Univ, Ctr Theoret Biol Phys, Houston, TX 77251 USA

[3] Rice Univ, Dept Chem, Houston, TX 77251 USA

[4] Paderborn Univ, Dept Math, Paderborn, Germany

[5] Zuse Inst Berlin, Berlin, Germany

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2020年 / 406卷

基金：

美国国家科学基金会;

关键词：

Data-driven methods; Koopman operator; Infinitesimal generator; System identification; Coarse graining; Control; STOCHASTIC DIFFERENTIAL-EQUATIONS; PREDICTIVE CONTROL; OPERATOR; DECOMPOSITION; CONVERGENCE; PROJECTION;

D O I：

10.1016/j.physd.2020.132416

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions, and modes of the generator and for system identification. In addition to learning the governing equations of deterministic systems, which then reduces to SINDy (sparse identification of nonlinear dynamics), it is possible to identify the drift and diffusion terms of stochastic differential equations from data. Moreover, we apply gEDMD to derive coarse-grained models of highdimensional systems, and also to determine efficient model predictive control strategies. We highlight relationships with other methods and demonstrate the efficacy of the proposed methods using several guiding examples and prototypical molecular dynamics problems. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：15

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