A Practical Identifiability Criterion Leveraging Weak-Form Parameter Estimation

Area of Science:

• Systems Biology
• Control Theory
• Differential Algebra

Background:

• Parameter estimation is crucial for understanding complex systems.
• Existing identifiability criteria may not fully capture the impact of data noise and estimator errors.
• Partially observed systems present unique challenges in parameter estimation.

Purpose of the Study:

• To define a novel, practical identifiability criterion, (e, q)-identifiability.
• To demonstrate the criterion's effectiveness in challenging identifiability studies.
• To introduce a computationally efficient method for assessing practical identifiability.

Main Methods:

• Developed the (e, q)-identifiability criterion, incorporating noise (e) and mean-square error (q).
• Applied differential algebra techniques to generate weak-form input-output equations.
• Utilized the Weak form Estimation of Nonlinear Dynamics (WENDy) for parameter estimation.

Main Results:

• The (e, q)-identifiability criterion effectively evaluates parameter estimate quality under varying noise levels.
• Weak-form equation error methods, particularly WENDy, provide faster identifiability assessment than output error methods.
• The proposed methods were successfully demonstrated on two biological modeling examples.

Conclusions:

• The (e, q)-identifiability criterion offers a more comprehensive assessment of practical identifiability.
• WENDy provides a computationally efficient and noise-robust approach for parameter estimation in systems with unobserved variables.
• This work enhances the ability to perform reliable parameter estimation and identifiability analysis in complex dynamical systems.