标题： 用于生物学中数学模型实用可辨识性分析的系统计算框架 显示英文标题

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

摘要： 实际可辨识性是数据驱动数学系统建模中的一个关键问题。 在本文中，我们提出了一种新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。 从实际可辨识性的严格数学定义出发，我们证明了其与费舍尔信息矩阵的可逆性等价。 我们的框架建立了实际可辨识性与坐标可辨识性之间的关系，引入了一种新的度量方法，相比轮廓似然方法，该方法简化并加速了参数可辨识性的评估。 此外，我们引入了新的正则化项以处理不可辨识的参数，从而实现不确定性量化并提高模型的可靠性。 为了指导实验设计，我们提出了一种最优数据收集算法，确保所有模型参数都是实际可辨识的。 对Hill函数、神经网络和动态生物模型的应用表明，所提出的计算框架在揭示关键生物过程和识别关键可观测变量方面具有可行性和效率。 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.