Forcing Function Diagnostics for Nonlinear Dynamics

Summary .  This article investigates the problem of model diagnostics for systems described by nonlinear ordinary differential equations (ODEs). I propose modeling lack of fit as a time-varying correction to the right-hand side of a proposed differential equation. This correction can be described as being a set of additive forcing functions, estimated from data. Representing lack of fit in this manner allows us to graphically investigate model inadequacies and to suggest model improvements. I derive lack-of-fit tests based on estimated forcing functions. Model building in partially observed systems of ODEs is particularly difficult and I consider the problem of identification of forcing functions in these systems. The methods are illustrated with examples from computational neuroscience.