How do you extract low order representations of complex systems from a series of observations?
This post outlines how you can use principal components to extract coherent structures from increasingly complex systems.
http://dataminingtheworld.blogspot.com.au/2014/04/flow-over-aircraft-and-wind-turbines.html
The answer is that, absent any further information, it's impossible. You need to have some idea of *what* the dynamics of the ``complex system'' is, and an idea of what
*physical quantity*, that describes some property of the system, can play the role for an ``order parameter'. To make sense of *that* it's necessary to have some idea of what are the processes one is interested in. If it's a social system, it could be described by game theory with the payoff of the players as order parameters, for example. If it's a magnetic system it would be the fluctuations of the magnetization and so on. To talk of coherent structures, it's necessary to have some idea of what these structures should describe in a given context and *why* some ``coherence'' might be expected.
While the same mathematical descriptions can be appropriate for understanding many different physical systems, simply by changing the names of the varables involved, the relevance of the mathematical description must be founded on the individual system.
So what one needs is to specify, at some scale, what are the symmetries of the system, under what transformations certain properties of the system don't change.
Somewhere *content* has to be introduced.
Indeed-but, even here, the *assumption* is that there is a specific dynamics. If you just have a time series and nothing more, you can easily get led astray, as Osborn and Provenzale have stressed, cf., also, this paper: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.5980
You can't extract insight in a content free way. What must be stressed is, *given* some (class of) problems, that *do* have ``interesting'' features, how is it possible to focus on *these* features? And then we can get into a discussion that shows that, using knowledge and experience from many different such clsses, some common themes emerge. I don't think it's useful to *start* with some technique and *then* look for a problem.
- Badges
- Science topic
- Similar topics
- Engineering
- Mechanical Engineering