Dynamical State and Parameter Estimation (Invited)

In building models of complex systems and networks, one has sparse measurements from which one must infer unknown parameters at the nodes and links as well as the unobserved state of the system if predictions are to be made. When these systems are nonlinear chaotic oscillations of the networks impede the ability to achieve these goals, and one must regularize the procedure to stabilize the transmission of information from the observations to the model. We will discuss this in a general context and demonstrate how the solution works in practice in the context of electronic circuits, and for a small geophysical model. We also consider the formulation of this problem for when there is noisy data, errors in the model, and uncertain initial conditions. This formulation is a statistical physics problem, and we demonstrate that the effective action for this problem is a systematic way to evaluate all the conditional means and covariances required for the estimations.