SYMBOL STATISTICS AND SPATIOTEMPORAL SYSTEMS

We consider the problem of estimating parameters from time-series obse rvations of spatio-temporal systems. Two types of models are considere d: (a) a one-dimensional coupled map lattice with nearest neighbor dif fusive coupling; and (b) the complex Ginzburg-Landau equation in one a nd two spatial dimensions. Model parameters are to be estimated using time-series observations from only a few sites. A symbolic partition o f the time series is introduced and the probabilities of observing var ious symbol sequences in the data are measured. The parameter fitting is accomplished by adjusting parameters of the model until it produces time series whose symbol sequences have the same probabilities as the data. We show that it is possible to reliably estimate the parameters from a single time series when the spatio-temporal dynamics is ''turb ulent'', i.e. it displays a wide range of space and time scales with n o discernible patterns.