Title: Learning Large Scale Ordinary Differential Equation Systems,
Abstract: Learning large scale nonlinear ordinary differential equation (ODE) systems
from data is known to be computationally and statistically challenging. We
present a framework together with the adaptive integral matching (AIM)
algorithm for learning polynomial or rational ODE systems with a sparse network
structure. The framework allows for time course data sampled from multiple
environments representing e.g. different interventions or perturbations of the
system. The algorithm AIM combines an initial penalised integral matching step
with an adapted least squares step based on solving the ODE numerically. The R
package episode implements AIM together with several other algorithms and is
available from CRAN. It is shown that AIM achieves state-of-the-art network
recovery for the in silico phosphoprotein abundance data from the eighth DREAM
challenge with an AUROC of 0.74, and it is demonstrated via a range of
numerical examples that AIM has good statistical properties while being
computationally feasible even for large systems.