A Joint estimation approach to sparse additive ordinary differential equations.

Area of Science:

• Statistics
• Applied Mathematics
• Computational Science

Background:

• Ordinary differential equations (ODEs) are fundamental for modeling complex system dynamics across various scientific disciplines.
• Existing methods often assume Gaussian observations, limiting their applicability to a broader range of real-world data.
• Sparse additive models offer a flexible framework for capturing complex relationships within ODE systems.

Purpose of the Study:

• To develop a novel joint estimation approach for generalized sparse additive ODEs accommodating non-Gaussian observations.
• To integrate likelihood, ODE fidelity, and sparse regularization into a unified framework.
• To provide a robust and efficient computational method for analyzing complex dynamical systems.

Main Methods:

• A novel joint estimation approach is proposed, unifying likelihood, ODE fidelity, and sparse regularization.
• The method is compatible with existing collocation techniques for ODE approximation.
• A block coordinate descent algorithm is designed to optimize the non-convex and non-differentiable objective function.

Main Results:

• The proposed method demonstrates superior performance in parameter estimation compared to existing approaches.
• The block coordinate descent algorithm guarantees global convergence.
• The approach effectively identifies the sparse structure within the additive ODE components.
• Simulation studies and real-world applications validate the method's efficacy.

Conclusions:

• The developed joint estimation method offers a powerful tool for analyzing complex systems with non-Gaussian data.
• The unified framework enhances both the accuracy of parameter estimation and the interpretability of ODE models.
• This work advances the state-of-the-art in statistical inference for differential equations.