A Systematic Computational Framework for Practical Identifiability Analysis in Mathematical Models Arising from Biology.

Practical identifiability is a fundamental challenge in the data-driven modeling of biological systems, as many model parameters cannot be directly measured and must be estimated from experimental data. Without confirming the identifiability of these parameters, model predictions may be unreliable, limiting their usefulness for understanding biological mechanisms or informing experimental and clinical decisions. In this paper, a novel mathematical framework is proposed for practical identifiability analysis in dynamic models. Starting from a rigorous mathematical definition, it is proved that practical identifiability is equivalent to the invertibility of the Fisher Information Matrix (FIM). The relationship between practical identifiability and coordinate identifiability is further established, introducing an efficient metric that simplifies and accelerates identifiability assessment compared to traditional profile likelihood methods. To address non-identifiable parameters, new regularization terms are incorporated, enabling uncertainty quantification and improving model reliability. Additionally, an optimal experimental design algorithm is developed to ensure all parameters are practically identifiable from collected data. Applications to Hill functions, neural networks, and biological models demonstrate the effectiveness and computational efficiency of the proposed framework in uncovering critical biological processes and identifying key observable variables.