Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 384, Issue -, Pages 200-221Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2019.01.030
Keywords
Ordinary differential equation; Differential-algebraic equation; Measurement data; Data-driven discovery; Regression; Sequential approximation
Funding
- AFOSR [FA95501810102]
- NSF [DMS 1418771]
- U.S. Department of Defense (DOD) [FA95501810102] Funding Source: U.S. Department of Defense (DOD)
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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.
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