  This article presents the MAGI software package for the inference of dynamic
systems. The focus of MAGI is on dynamics modeled by nonlinear ordinary
differential equations with unknown parameters. While such models are widely
used in science and engineering, the available experimental data for parameter
estimation may be noisy and sparse. Furthermore, some system components may be
entirely unobserved. MAGI solves this inference problem with the help of
manifold-constrained Gaussian processes within a Bayesian statistical
framework, whereas unobserved components have posed a significant challenge for
existing software. We use several realistic examples to illustrate the
functionality of MAGI. The user may choose to use the package in any of the R,
MATLAB, and Python environments.
