Predicting low-dimensional spatiotemporal dynamics using discrete wavelet transforms

A method is presented for predicting spatiotemporal time series whose dynamics is generated by a low-dimensional deterministic dynamical system. It is based on a combination of time delay embedding and wavelet expansion and is also applicable in cases where the dynamics may not be linearly decomposed into the evolution of a small number of spatial modes. As an example, we predict chaotic transversal motions of two Gaussian pulses along a one-dimensional axis.