Convergence of Weak-SINDy Surrogate Models

IF 1.7 4区 数学 Q2 MATHEMATICS, APPLIED SIAM Journal on Applied Dynamical Systems Pub Date : 2024-04-03 DOI:10.1137/22m1526782
Benjamin P. Russo, M. Paul Laiu
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Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 2, Page 1017-1051, June 2024.
Abstract.In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of nonlinear system identification techniques, namely SINDy, weak-SINDy, and the occupation kernel method. Under the assumption that the dynamics are a finite linear combination of a set of basis functions, these methods establish a linear system to recover coefficients. We illuminate the structural similarities between these techniques and establish a projection property for the weak-SINDy technique. Following the overview, we analyze the error of surrogate models generated by a simplified version of weak-SINDy. In particular, under the assumption of boundedness of a composition operator given by the solution, we show that (i) the surrogate dynamics converges towards the true dynamics and (ii) the solution of the surrogate model is reasonably close to the true solution. Finally, as an application, we discuss the use of a combination of weak-SINDy surrogate modeling and proper orthogonal decomposition (POD) to build a surrogate model for partial differential equations (PDEs).
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弱 SINDy 代用模型的收敛性
SIAM 应用动力系统期刊》,第 23 卷第 2 期,第 1017-1051 页,2024 年 6 月。摘要.在本文中,我们对非线性动力学稀疏识别(SINDy)方法的一个变体生成的代用模型进行了深入的误差分析。我们首先概述了各种非线性系统识别技术,即 SINDy、弱 SINDy 和占位核方法。在动力学是一组基函数的有限线性组合的假设下,这些方法建立了一个线性系统来恢复系数。我们阐明了这些技术之间的结构相似性,并为弱 SINDy 技术建立了投影属性。概览之后,我们分析了弱 SINDy 简化版生成的代用模型的误差。特别是,在解给出的组成算子有界的假设下,我们证明了:(i) 代用动态收敛于真实动态;(ii) 代用模型的解合理地接近真实解。最后,作为应用,我们讨论了如何将弱 SINDy 代理建模与适当正交分解 (POD) 结合使用,以建立偏微分方程 (PDE) 的代理模型。
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来源期刊
SIAM Journal on Applied Dynamical Systems
SIAM Journal on Applied Dynamical Systems 物理-物理:数学物理
CiteScore
3.60
自引率
4.80%
发文量
74
审稿时长
6 months
期刊介绍: SIAM Journal on Applied Dynamical Systems (SIADS) publishes research articles on the mathematical analysis and modeling of dynamical systems and its application to the physical, engineering, life, and social sciences. SIADS is published in electronic format only.
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