Inferring mechanism from time-series data: Delay-differential equations

When there is qualitative information about the underlying professes and structure of a dynamical system, it may be possible to infer very accurate quantitative information about these processes using only an output rime series from the system. We illustrate how this can be accomplished for time series data from a delay-differential equation with a single fixed delay. Our approach exploits modem techniques for non-parametric function estimation, is robust to fairly high levels of dynamic noise and measurement error, and can be extended straightforwardly to more general delay-differential systems and multivariate systems.