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

Area of Science:

• Dynamical systems modeling
• Computational mathematics
• Statistical inference

Background:

• Ordinary differential equations (ODEs) are crucial for modeling complex system dynamics.
• Existing frequentist methods struggle with uncertainty quantification in parameter estimation for high-dimensional sparse ODEs.
• Noisy time-course data presents challenges for accurate system structure identification.

Purpose of the Study:

• To develop a Bayesian hierarchical collocation method for improved uncertainty quantification in ODE modeling.
• To enable simultaneous system identification and trajectory estimation from noisy data.
• To address limitations of frequentist approaches in parameter estimation uncertainty.

Main Methods:

• A Bayesian hierarchical collocation framework is proposed.
• The method integrates likelihood, ODE constraints, and a group-wise sparse penalty.
• It operates under an additive ODE model assumption.

Main Results:

• The proposed Bayesian method demonstrates favorable performance in simulation studies.
• It achieves better quantification of uncertainty compared to existing methods.
• Accurate system trajectories and additive components were recovered.

Conclusions:

• The Bayesian hierarchical collocation method offers a robust approach for ODE system identification.
• It effectively handles noisy time-course data and enhances uncertainty quantification.
• The methodology is applicable to real-world systems, such as gene regulatory networks.