标题： 一个系统化的计算框架用于生物领域数学模型的实际可辨识性分析 显示英文标题

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

摘要： 实际可辨识性是在基于数据的数学系统建模中的一个关键问题。 本文提出了一种新颖的实际可辨识性分析框架，用于评估生物系统数学模型中的参数可辨识性。 从严格定义实际可辨识性的数学定义出发，我们证明了它与Fisher信息矩阵可逆性之间的等价性。 我们的框架建立了实际可辨识性和坐标可辨识性之间的关系，并引入了一种新度量，相比轮廓似然法能简化且加速参数可辨识性的评估。 此外，我们提出了新的正则化项来处理非可辨识参数，从而实现不确定性量化并提升模型可靠性。 为了指导实验设计，我们提供了一种最优数据收集算法，确保所有模型参数都能达到实际可辨识性。 Hill函数、神经网络以及动态生物模型的应用展示了所提出的计算框架在揭示关键生物学过程和识别关键可观测变量方面的可行性和效率。 显示英文摘要

摘要： Practical identifiability is a critical concern in data-driven modeling of mathematical systems. In this paper, we propose a novel framework for practical identifiability analysis to evaluate parameter identifiability in mathematical models of biological systems. Starting with a rigorous mathematical definition of practical identifiability, we demonstrate its equivalence to the invertibility of the Fisher Information Matrix. Our framework establishes the relationship between practical identifiability and coordinate identifiability, introducing a novel metric that simplifies and accelerates the evaluation of parameter identifiability compared to the profile likelihood method. Additionally, we introduce new regularization terms to address non-identifiable parameters, enabling uncertainty quantification and improving model reliability. To guide experimental design, we present an optimal data collection algorithm that ensures all model parameters are practically identifiable. Applications to Hill functions, neural networks, and dynamic biological models demonstrate the feasibility and efficiency of the proposed computational framework in uncovering critical biological processes and identifying key observable variables.