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, we propose a novel mathematical framework for practical identifiability analysis in dynamic models. Starting from a rigorous mathematical definition, we prove that practical identifiability is equivalent to the invertibility of the Fisher Information Matrix (FIM). We further establish the relationship between practical identifiability and coordinate identifiability, introducing an efficient metric that simplifies and accelerates identifiability assessment compared to traditional profile likelihood methods. To address non-identifiable parameters, we incorporate new regularization terms, enabling uncertainty quantification and improving model reliability. Additionally, we develop an optimal experimental design algorithm 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.