Model reconstruction of nonlinear dynamical systems driven by noise

Most natural and man-made systems are inherently noisy and nonlinear. This has led to the use of stochastic nonlinear dynamical models for observed phenomena across many scientific disciplines. Examples range from lasers [1] and molecular motors [2], to epidemiology [3] , to coupled matter–radiation systems in astrophysics [4]. In this approach a complex system is characterized by projecting it onto a specific dynamical model with parameters obtained from the measured time-series data. In a great number of important problems the model is not usually known exactly from “first principles” and one is faced with a rather broad range of possible parametric models to consider. Furthermore, important “hidden” features of a model such as coupling coefficients between the dynamical degrees of freedom can be very difficult to extract due to the intricate interplay between noise and nonlinearity. These obstacles render the inference of stochastic nonlinear dynamical models from experimental time series a formidable task, with no efficient general methods currently available for its solution. Deterministic inference techniques [5] consistently fail to yield accurate parameter estimates in the presence of noise. The problem becomes even more complicated when both measurement noise as well as intrinsic dynam