Maximum entropy approach to nonlinear modeling

We present a technique for building deterministic models of the nonlinear dynamics underlying observed time series. It is formulated from maximum entropy principle within the framework of information theory. Two numerical examples of chaotic time series illustrate the method. Furthermore, the theory on which the method is based, provides an entropy-like quantity that characterizes the suitability of the model. It is defined over the space of parameters of the model. We illustrate, with two applications, how this entropy can be a useful tool for exploring the phase space, and establishing a criterion for choosing a convenient parametrized functional form