Estimation And Variable Selection For Sparse High-dimensional Ordinary Differential Equation

Ordinary Differential Equation(ODE)models are widely utilized to describe com-plicated dynamical systems,such as the gene regulation network.Existing methods for estimating the high-dimensional ODE models often rely on dense observed data,yet the data generated by some dynamical system is sparse.In this paper,we propose a new method for high-dimensional ODE models under sparse design.Specifically,combing the functional principal component analysis(FPCA)and variable selection techniques,we can recover the relation network of the state variables in high-dimensional ODE models.Sim-ulation studies are performed to show that the proposed approach has a good finite sample property.Meanwhile,the asymptotic properties of the proposed method are established.