A Joint estimation approach to sparse additive ordinary differential equations

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.

Automated summary

Ordinary differential equations (ODEs) are commonly used in real applications to describe the dynamics of complex systems. In this article, we propose a novel joint estimation approach for generalized sparse additive ODEs, allowing for non-Gaussian observations. The method considers likelihood, ODE fidelity, and sparse regularization simultaneously, and is optimized using a block coordinate descent algorithm for non-convex and non-differentiable objective functions. The global convergence of the algorithm is established, and simulation studies and two applications demonstrate the superior performance of the method in estimation and identifying sparse structures.