文件列表:

Common.zip (53182, 2006-10-30)
Mg17.zip (197117, 2006-10-30)
MG17Lyapunov.zip (11332, 2006-10-30)
RefutationES.pdf (146624, 2005-12-09)

In this package you find the following items: 1. Folder MG17 (zipped) Contains the Matlab code I used for the chaotic attractor prediction documented in the paper H. Jaeger and H. Haas, Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication. Science 304, 2 April 2004 Together with the helper functions from the folder common, this provides a complete Matlab package for re-running the simulations from the Science paper. 2. RefutationES.pdf A text document in which I refute the objections of a Science reviewer who objected that the Mackey-Glass data that I used might be generated incorrectly and in fact not be chaotic. This is of interest only for those with a deeper interest in the subtelties of chaotic time series simulation. 3. Folder MG17Lyapunov (zipped) Matlab code for checking the leading Lyapunov exponent for the Mackey-Glass time series that I generated for the investigations documented in the Science paper. This again will be of interest only for those with a deeper interest in the subtelties of chaotic time series simulation. 4. Folder common (zipped) Some Matlab helper routines that are called by functions and scripts in MG17 and MG17Lyapunov. Make sure that these helpers are in your Matlab search paths when you work with MG17 or MG17Lyapunov. General comment. I have received a number of messages from people who were unable to replicate the results reported in the Science paper. These problems apparently are mostly due to improper generation of the training and testing data. Specifically, if one uses the delay differential equation solvers that come shipped with Matlab for generating Mackey-Glass data, their quality is insufficient because the Matlab solvers are precise only on far-spaced support points, with unreliable interpolated values in between. The inaccuracies are large enough to disrupt the high-precision prediction possible with ESNs. Therefore I used self-generated Mackey-Glass data for training and testing, whose setup (and quality assessment) is detailed out in the document RefutationES.pdf. -- Another possible reason why some may have difficulties with replicating the Science paper results is that they might not use long enough washout times for the dynamical reservoir. Make sure that both in training and testing, about 1,000 iterations are "wasted" before network states are used for training output weights or making predictions (if one uses networks as large as 1,000 units).

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