标题： 广义灵敏度函数用于尺寸结构种群模型 显示英文标题

标题： Generalized sensitivity functions for size-structured population models

摘要： 结构尺寸种群模型提供了一种流行的方法，用于数学描述如细菌聚集、鱼群和星子演化等现象。 对于参数估计，广义敏感性函数（GSFs）提供了一种量化实验域特定区域数据影响的工具。 这些函数有助于识别最相关的数据子域，从而增强实验设计的优化。 据我们所知，GSFs尚未在偏微分方程（PDE）领域中使用，因此我们提供了Thomaseth和Cobelli以及Banks等人的离散和连续常微分方程（ODE）概念的新型PDE扩展。 我们在结构尺寸种群模型的背景下分析GSFs，并特别分析Smoluchowski凝聚方程，以确定三种不同凝聚核在时间与体积域中的最相关区域。 最后，我们提供了证据，表明Smoluchowski凝聚方程的参数估计不需要凝胶后数据。 显示英文摘要

摘要： Size-structured population models provide a popular means to mathematically describe phenomena such as bacterial aggregation, schooling fish, and planetesimal evolution. For parameter estimation, generalized sensitivity functions (GSFs) provide a tool that quantifies the impact of data from specific regions of the experimental domain. These functions help identify the most relevant data subdomains, which enhances the optimization of experimental design. To our knowledge, GSFs have not been used in the partial differential equation (PDE) realm, so we provide a novel PDE extension of the discrete and continuous ordinary differential equation (ODE) concepts of Thomaseth and Cobelli and Banks et al. respectively. We analyze the GSFs in the context of size-structured population models, and specifically analyze the Smoluchowski coagulation equation to determine the most relevant time and volume domains for three, distinct aggregation kernels. Finally, we provide evidence that parameter estimation for the Smoluchowski coagulation equation does not require post-gelation data.