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 linear reaction-advection-diffusion (RAD) PDE models. We show that the differential algebra approach can always, in theory, be applied to linear RAD 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 structural identifiability. Finally, we show that our approach can also be applied to a class of non-linear PDE models that are linear in the unobserved variables, and conclude by discussing future possibilities and computational cost of performing structural identifiability analysis on more general PDE models in mathematical biology.

翻译：数学模型在解析生物数据及做出精准预测中，常需确保模型参数具有可辨识性。针对常微分方程模型的结构可辨识性评估方法已较为成熟，但尚无普遍适用的方法可评估偏微分方程（PDE）模型——这类模型对于捕捉众多现象中的空间特征至关重要——的结构可辨识性。最近，微分代数方法已被证明可应用于若干特定PDE模型的结构可辨识性分析。在本篇短文里，我们提出一种通用方法论，用于对部分观测的线性反应-平流-扩散（RAD）PDE模型进行结构可辨识性分析。我们证明，在理论上，微分代数方法始终可应用于线性RAD模型。此外，尽管平流项与扩散项的引入增加了复杂性，但非空间模型的空间对应项的可辨识性并不会降低其结构可辨识性。最后，我们展示该方法还可应用于一类在未观测变量上呈线性关系的非线性PDE模型，并探讨了在数学生物学中推广至更一般PDE模型时进行结构可辨识性分析的未来可能性与计算成本。