Continuous-time nonlinear signal processing: A neural network based approach for gray box identification

Artificial neural networks (ANNs) are often used for short term discrete time series predictions. Continuous-time models are, however, required for qualitatively correct approximations to long-term dynamics (attractors) of nonlinear dynamical systems and their transitions (bifurcations) as system parameters are varied. In previous work we developed a black-box methodology for the characterization of experimental time series as continuous-time models (sets of ordinary differential equations) based on a neural network platform. This methodology naturally lends itself to the identification of partially known first principles dynamic models, and here we present its extension to `gray-box' identification.