期刊
MULTISCALE MODELING & SIMULATION
卷 15, 期 3, 页码 1108-1129出版社
SIAM PUBLICATIONS
DOI: 10.1137/16M1086637
关键词
dynamical systems; system identification; compressed sensing; sparse representation; l(1)-minimization; splitting optimization methods; chaotic systems; ergodic theory
资金
- NSF CAREER grant [1255631]
- AFOSR YIP grant [FA9550-13-1-0125]
- Fall Moncrief Grand Challenge Faculty Award
Learning the governing equations in dynamical systems from time-varying measurements is of great interest across different scientific fields. This task becomes prohibitive when such data is moreover highly corrupted, for example, due to the recording mechanism failing over unknown intervals of time. When the underlying system exhibits chaotic behavior, such as sensitivity to initial conditions, it is crucial to recover the governing equations with high precision. In this work, we consider continuous time dynamical systems (x) over dot = f(x) where each component of f : R-d -> R-d is a multivariate polynomial of maximal degree p; we aim to identify f exactly from possibly highly corrupted measurements x(t(1)), x(t(2)), . . . , x(t(m)). As our main theoretical result, we show that if the system is sufficiently ergodic that this data satisfies a strong central limit theorem (as is known to hold for chaotic Lorenz systems), then the governing equations f can be exactly recovered as the solution to an l(1) minimization problem-even if a large percentage of the data is corrupted by outliers. Numerically, we apply the alternating minimization method to solve the corresponding constrained optimization problem. Through several examples of three-dimensional chaotic systems and higher dimensional hyperchaotic systems, we illustrate the power, generality, and efficiency of the algorithm for recovering governing equations from noisy and highly corrupted measurement data.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据