Global parameter identifiability is a property of a parametric ODE model to recover the parameter values uniquely from the input-output data. Not all parametric ODE models have this property, and checking for parameter identifiability is a prerequisite to perform numerical parameter estimation. There are many algorithms and software packages for global parameter identifiability, and frequently the runtime is large. However, the computational complexity for this problem has not been analyzed yet, though there are complexity results for local (finitely many values fit the data) parameter identifiability. In this paper, we estimate the complexity of checking global parameter identifiability over real fields for ODE models that depend linearly on the state variables and rationally on the parameters. In particular, we prove that it is equivalent to the injectivity problem.

翻译：全局参数可辨识性是参数化常微分方程模型从输入输出数据中唯一恢复参数值的一种性质。并非所有参数化ODE模型都具有这一性质，且在数值参数估计之前，检查参数的可辨识性是一项必要前提。目前已有多种用于全局参数可辨识性的算法和软件包，其运行时间通常较长。然而，尽管对于局部（即有限个值符合数据）参数可辨识性已有复杂性结果，但该问题的计算复杂性尚未得到分析。本文中，我们估算了在实数域上检查依赖于状态变量线性且参数有理的ODE模型全局参数可辨识性的复杂性。特别地，我们证明了该问题等价于单射性问题。