Differential equation models are crucial to scientific processes. The values of model parameters are important for analyzing the behaviour of solutions. A parameter is called globally identifiable if its value can be uniquely determined from the input and output functions. To determine if a parameter estimation problem is well-posed for a given model, one must check if the model parameters are globally identifiable. This problem has been intensively studied for ordinary differential equation models, with theory and several efficient algorithms and software packages developed. A comprehensive theory of algebraic identifiability for PDEs has hitherto not been developed due to the complexity of initial and boundary conditions. Here, we provide theory and algorithms, based on differential algebra, for testing identifiability of polynomial PDE models. We showcase this approach on PDE models arising in the sciences.

翻译：微分方程模型对科学过程至关重要。模型参数的值对于分析解的行为具有重要意义。若参数的值可由输入和输出函数唯一确定，则称该参数为全局可辨识的。要判定给定模型的参数估计问题是否适定，必须检验模型参数是否全局可辨识。该问题在常微分方程模型中已得到深入研究，发展出了成熟的理论、多种高效算法及软件包。由于初边值条件的复杂性，偏微分方程模型的代数可辨识性此前尚未形成系统的理论。本文基于微分代数提出了一套检验多项式偏微分方程模型可辨识性的理论与算法，并以科学领域中的偏微分方程模型为例展示了该方法的应用。