论随机 SINDy 的高阶漂移和扩散估计值

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-14 DOI:10.1137/23m1567011

Mathias Wanner, Igor Mezić

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引用次数: 0

摘要

SIAM 应用动力系统期刊》，第 23 卷第 2 期，第 1504-1539 页，2024 年 6 月。摘要.非线性动力学稀疏识别（SINDy）算法可应用于随机微分方程（SDEs），使用来自 SDE 实现的数据估计漂移和扩散函数。SINDy 算法需要每个函数的样本数据，而样本数据通常是通过状态数据进行数值估计的。我们分析了之前提出的漂移和扩散函数估计值的性能，给出了有限数据的误差界限。然而，由于这种算法只有在采样频率和轨迹长度都达到无穷大时才会收敛，因此在一定容差范围内获得近似值可能是不可行的。为了解决这个问题，我们开发了精度更高的估计值，供 SINDy 框架使用。对于给定的采样频率，这些估计值能给出更精确的漂移和扩散函数近似值，从而使 SINDy 成为更可行的系统识别方法。

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On Higher Order Drift and Diffusion Estimates for Stochastic SINDy

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 2, Page 1504-1539, June 2024.
Abstract.The sparse identification of nonlinear dynamics (SINDy) algorithm can be applied to stochastic differential equations (SDEs) to estimate the drift and the diffusion function using data from a realization of the SDE. The SINDy algorithm requires sample data from each of these functions, which is typically estimated numerically from the data of the state. We analyze the performance of the previously proposed estimates for the drift and the diffusion function to give bounds on the error for finite data. However, since this algorithm only converges as both the sampling frequency and the length of trajectory go to infinity, obtaining approximations within a certain tolerance may be infeasible. To combat this, we develop estimates with higher orders of accuracy for use in the SINDy framework. For a given sampling frequency, these estimates give more accurate approximations of the drift and diffusion functions, making SINDy a far more feasible system identification method.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.