博文
Predicting Catastrophes in nonlinear Dynamical Systems
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师弟王延博士来组讨论，谈及Wen-Xu Wang等新近之作。
PRL 106, 154101 (2011)
Predicting Catastrophes in Nonlinear Dynamical Systems by Compressive Sensing
Abstract:An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems
under the assumption that the system equations are completely unknown and only time series reflecting
the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field
or map of the underlying system into a suitable function series and then to use the compressive-sensing
technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic
systems are provided to demonstrate our idea.
under the assumption that the system equations are completely unknown and only time series reflecting
the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field
or map of the underlying system into a suitable function series and then to use the compressive-sensing
technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic
systems are provided to demonstrate our idea.
另一篇文章：EPL, 94 (2011) 48006
Time-series–based prediction of complex oscillator networks via compressive sensing
Abstract – Complex dynamical networks consisting of a large number of interacting units are
ubiquitous in nature and society. There are situations where the interactions in a network of
interest are unknown and one wishes to reconstruct the full topology of the network through
measured time series. We present a general method based on compressive sensing. In particular, by
using power series expansions to arbitrary order, we demonstrate that the network-reconstruction
problem can be casted into the form X=G· a, where the vector X and matrix G are determined
by the time series and a is a sparse vector to be estimated that contains all nonzero power series
coefficients in the mathematical functions of all existing couplings among the nodes. Since a is
sparse, it can be solved by the standard L1-norm technique in compressive sensing. The main
advantages of our approach include sparse data requirement and broad applicability to a variety
of complex networked dynamical systems, and these are illustrated by concrete examples of model
and real-world complex networks.
ubiquitous in nature and society. There are situations where the interactions in a network of
interest are unknown and one wishes to reconstruct the full topology of the network through
measured time series. We present a general method based on compressive sensing. In particular, by
using power series expansions to arbitrary order, we demonstrate that the network-reconstruction
problem can be casted into the form X=G· a, where the vector X and matrix G are determined
by the time series and a is a sparse vector to be estimated that contains all nonzero power series
coefficients in the mathematical functions of all existing couplings among the nodes. Since a is
sparse, it can be solved by the standard L1-norm technique in compressive sensing. The main
advantages of our approach include sparse data requirement and broad applicability to a variety
of complex networked dynamical systems, and these are illustrated by concrete examples of model
and real-world complex networks.
除了其核心部分，其他粗粗地看了一下，有如下感觉：
1.作者善为文；
2.问遍身边网上的朋友也不知道compressive sensing如何翻译成中文，但关于这个方法的应用和原理的文章很多可见http://dsp.rice.edu/cs；
3. 问题：如果有一个网络，并非全部结点的时间序列都知道，那么对于已知的结点和时序，用所给出的方法的准确性会有怎么样的变化。如果将“遗漏”信息作为“噪声”，可想而知的是“Our method is robust against noise, due to the optimization nature of the compressive-sensing method.”但从抗噪声的工作来看，一般都是弱噪声才成。所以“遗漏”不能太多。
4. 在非线性化学实验中，如果将关心的反应物或中间产物的时间序列测量得到，那么相应的化学反应速率常数完全可以用这种方法给出。不知道以前组内师弟(妹)们是如何估计这些常数的。
5. 多讨论才能知道更多的相关信息。
https://blog.sciencenet.cn/blog-374356-446892.html
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