Because of the increasing diversity of data sets and measurement techniques in biology, a growing spectrum of modeling methods is being developed. It is generally recognized that it is critical to pick the appropriate method to exploit the amount and type of biological data available for a given system. Here, we describe a method for use in situations where temporal data from a network is collected over multiple time points, and in which little prior information is available about the interactions, mathematical structure, and statistical distribution of the network. Our method results in models that we term Nonparametric exterior derivative estimation Ordinary Differential Equation (NODE) model's. We illustrate the method's utility using spatiotemporal gene expression data from Drosophila melanogaster embryos. We demonstrate that the NODE model's use of the temporal characteristics of the network leads to quantifiable improvements in its predictive ability over nontemporal models that only rely on the spatial characteristics of the data. The NODE model provides exploratory visualizations of network behavior and structure, which can identify features that suggest additional experiments. A new extension is also presented that uses the NODE model to generate a comb diagram, a figure that presents a list of possible network structures ranked by plausibility. By being able to quantify a continuum of interaction likelihoods, this helps to direct future experiments.