  Ordinary differential equation (ODE) models are widely used to describe
chemical or biological processes. This article considers the estimation and
assessment of such models on the basis of time-course data. Due to experimental
limitations, time-course data are often noisy and some components of the system
may not be observed. Furthermore, the computational demands of numerical
integration have hindered the widespread adoption of time-course analysis using
ODEs. To address these challenges, we explore the efficacy of the recently
developed MAGI (MAnifold-constrained Gaussian process Inference) method for ODE
inference. First, via a range of examples we show that MAGI is capable of
inferring the parameters and system trajectories, including unobserved
components, with appropriate uncertainty quantification. Second, we illustrate
how MAGI can be used to assess and select different ODE models with time-course
data based on MAGI's efficient computation of model predictions. Overall, we
believe MAGI is a useful method for the analysis of time-course data in the
context of ODE models, which bypasses the need for any numerical integration.

Molecular Networks