The dynamic behavior of synthetic gene circuits plays a key role in ensuring their correct function. Although there has been substantial work on modeling dynamic behavior after circuit construction, the forward engineering of dynamic behavior remains a major challenge. Previous engineering methods have focused on quantifying average behaviors of circuits over an extended time window, however this provides a static characterization of behavior that is a poor predictor of dynamics. Here we present a method for characterizing the dynamic behavior of synthetic gene circuits, using parameter inference of dynamical system models applied to time-series measurements of cell cultures growing in microtiter plates. We demonstrate that the behaviors of simple devices can be characterized dynamically and used to predict the behaviors of more complex circuits. Specifically, we compose 23 biological parts into 9 devices and use them to design 9 synthetic gene circuits in E. coli that provide core functionality for engineering cell behavior at the population level, including relays, receivers and a degrader. We embody our method in a software package and corresponding programming language. Our method supports the notion of an inference graph for iterative inference of models as new circuits are constructed, without the need to infer all models from scratch, and lays the foundation for characterizing large libraries of synthetic gene circuits in a scalable manner.