Numerical aspects for approximating governing equations using data

JOURNAL OF COMPUTATIONAL PHYSICS

卷:384

Article

Wu, Kailiang¹  Xiu, Dongbin¹ 

[1] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA

关键词: Ordinary differential equation;    Differential-algebraic equation;    Measurement data;    Data-driven discovery;    Regression;    Sequential approximation;   

DOI  :  10.1016/j.jcp.2019.01.030

来源: Elsevier

【 摘 要 】

We present effective numerical algorithms for approximating unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high accuracy. Upon recasting the problem into a function approximation problem, we discuss several important aspects for accurate approximation. Most notably, we discuss the importance of using a large number of short bursts of trajectory data, rather than using data from a single long trajectory. Several options for the numerical algorithms to perform accurate approximation are then presented, along with an error estimate of the final equation approximation. We then present an extensive set of numerical examples of both linear and nonlinear systems to demonstrate the properties and effectiveness of our equation approximation algorithms. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free