  The use of differential equations (ODE) is one of the most promising
approaches to network inference. The success of ODE-based approaches has,
however, been limited, due to the difficulty in estimating parameters and by
their lack of scalability. Here we introduce a novel method and pipeline to
reverse engineer gene regulatory networks from gene expression of time series
and perturbation data based upon an improvement on the calculation scheme of
the derivatives and a pre-filtration step to reduce the number of possible
links. The method introduces a linear differential equation model with adaptive
numerical differentiation that is scalable to extremely large regulatory
networks. We demonstrate the ability of this method to outperform current
state-of-the-art methods applied to experimental and synthetic data using test
data from the DREAM4 and DREAM5 challenges. Our method displays greater
accuracy and scalability. We benchmark the performance of the pipeline with
respect to data set size and levels of noise. We show that the computation time
is linear over various network sizes.
