标题： 偏微分方程模型的代数可辨识性 显示英文标题

标题： Algebraic identifiability of partial differential equation models

摘要： 微分方程模型对于科学过程至关重要。 模型参数的值对于分析解的行为非常重要。 如果参数的值可以从输入和输出函数中唯一确定，则该参数称为全局可识别的。 为了确定给定模型的参数估计问题是否适定，必须检查模型参数是否全局可识别。 这个问题已经被深入研究，针对常微分方程模型，已经发展出了理论以及几种高效算法和软件包。 由于初始和边界条件的复杂性，迄今为止尚未发展出关于偏微分方程代数可识别性的完整理论。 在这里，我们基于微分代数提供理论和算法，用于测试多项式偏微分方程模型的可识别性。 我们将这种方法应用于科学中出现的偏微分方程模型。 显示英文摘要

摘要： 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.