Parameter identifiability is a structural property of an ODE model for recovering the values of parameters from the data (i.e., from the input and output variables). This property is a prerequisite for meaningful parameter identification in practice. In the presence of nonidentifiability, it is important to find all functions of the parameters that are identifiable. The existing algorithms check whether a given function of parameters is identifiable or, under the solvability condition, find all identifiable functions. Our first main result is an algorithm that computes all identifiable functions without any additional assumptions. Our second main result concerns the identifiability from multiple experiments. For this problem, we show that the set of functions identifiable from multiple experiments is what would actually be computed by input-output equation-based algorithms if the solvability condition is not fulfilled. We give an algorithm that not only finds these functions but also provides an upper bound for the number of experiments to be performed to identify these functions.

中文翻译：

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计算 ODE 模型的所有可识别函数

参数可识别性是用于从数据（即从输入和输出变量）恢复参数值的 ODE 模型的结构特性。此属性是在实践中进行有意义的参数识别的先决条件。在存在不可识别性的情况下，重要的是找到所有可识别参数的函数。现有算法检查给定的参数函数是否可识别，或者在可解性条件下找到所有可识别的函数。我们的第一个主要结果是一种无需任何额外假设即可计算所有可识别函数的算法。我们的第二个主要结果涉及多个实验的可识别性。对于这个问题，我们表明，如果不满足可解性条件，从多个实验中可识别的函数集实际上是由基于输入输出方程的算法计算的。我们给出的算法不仅可以找到这些函数，而且还提供了为识别这些函数而进行的实验数量的上限。