  Ordinary differential equations (ODEs) are widely used to characterize the
dynamics of complex systems in real applications. In this article, we propose a
novel joint estimation approach for generalized sparse additive ODEs where
observations are allowed to be non-Gaussian. The new method is unified with
existing collocation methods by considering the likelihood, ODE fidelity and
sparse regularization simultaneously. We design a block coordinate descent
algorithm for optimizing the non-convex and non-differentiable objective
function. The global convergence of the algorithm is established. The
simulation study and two applications demonstrate the superior performance of
the proposed method in estimation and improved performance of identifying the
sparse structure.
