Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are well-established for ordinary differential equation models, yet there are no commonly adopted approaches that can be applied to assess the structural identifiability of the partial differential equation (PDE) models that are requisite to capture spatial features inherent to many phenomena. The differential algebra approach to structural identifiability has recently been demonstrated to be applicable to several specific PDE models. In this brief article, we present general methodology for performing structural identifiability analysis on partially observed reaction-advection-diffusion (RAD) PDE models that are linear in the unobserved quantities. We show that the differential algebra approach can always, in theory, be applied to such models. Moreover, despite the perceived complexity introduced by the addition of advection and diffusion terms, identifiability of spatial analogues of non-spatial models cannot decrease in structural identifiability. We conclude by discussing future possibilities and the computational cost of performing structural identifiability analysis on more general PDE models.

翻译：数学模型的参数可识别性是有效解释生物数据并进行准确预测的关键前提。评估模型所谓结构可识别性的方法在常微分方程模型中已相当成熟，但对于捕捉许多现象固有空间特征的偏微分方程模型，目前尚无通用的评估方法。近年来，微分代数方法已被证明可应用于若干特定偏微分方程模型的结构可识别性分析。本文提出了一套通用方法，用于对部分观测的、关于未观测量为线性的反应-对流-扩散偏微分方程模型进行结构可识别性分析。我们证明，在理论上微分代数方法始终可应用于此类模型。此外，尽管对流项和扩散项的加入带来了感知上的复杂性，但非空间模型的空间对应物在结构可识别性上不会降低。最后，我们讨论了未来可能性及对更一般偏微分方程模型进行结构可识别性分析的计算成本。