A Bayesian collocation integral method for system identification of ordinary differential equations

Ordinary differential equations (ODEs) are widely considered for modeling the dynamics of complex systems across various scientific areas. To identify the structure of high-dimensional sparse ODEs from noisy time-course data, most existing methods adopt a frequentist perspective, while uncertainty quantification in parameter estimation remains challenging. Under an additive ODE model assumption, we present a Bayesian hierarchical collocation method to provide better quantification of uncertainty. Our framework unifies the likelihood, integrated ODE constraints and a group-wise sparse penalty, allowing for simultaneous system identification and trajectory estimation. We demonstrate the favorable performance of the proposed method through simulation studies, where the recovered system trajectories and estimated additive components are compared with other recent methods. A real data example of gene regulatory networks is provided to illustrate the methodology.