Structural identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence of noise. The method of input-output equations is one method for verifying structural identifiability. This method stands out in its importance because the additional insights it provides can be used to analyze and improve models. However, its complete theoretical grounds and applicability are still to be established. A subtlety and key for this method to work correctly is knowing whether the coefficients of these equations are identifiable. In this paper, to address this, we prove identifiability of the coefficients of input-output equations for types of differential models that often appear in practice, such as linear models with one output and linear compartment models in which, from each compartment, one can reach either a leak or an input. This shows that checking identifiability via input-output equations for these models is legitimate and, as we prove, that the field of identifiable functions is generated by the coefficients of the input-output equations. Finally, we exploit a connection between input-output equations and the transfer function matrix to show that, for a linear compartment model with an input and strongly connected graph, the field of all identifiable functions is generated by the coefficients of the transfer function matrix even if the initial conditions are generic.
翻译:结构性可识别性是一种差异模型的属性, 其参数允许在无噪音的情况下从模型方程式中确定参数。 输入输出方程式的方法是核实结构可识别性的一种方法。 这个方法之所以重要,是因为它所提供的额外见解可以用来分析和改进模型。 但是, 其完整的理论依据和适用性仍有待确定。 这个方法正确发挥作用的微妙性和关键在于知道这些方程式的系数是否可识别。 为了解决这个问题, 我们证明在实际中经常出现的不同模型类型输入- 输出方程式的系数是可以识别的, 例如, 一种输出模型和线形隔间模型的线性模型, 从每个间隔中可以达到泄漏或输入。 这表明, 通过输入- 输出方程式等方程式检查可识别性是正当的, 正如我们所证明的那样, 可识别功能的领域是由输入- 输出方程式的系数产生的。 最后, 我们利用输入- 输出方程式和转移方程式的系数之间的关联性系数, 在输入- 输入方程式和转移方程式功能之间, 如果输入方程式的初始性模型和转移功能是可识别的矩阵, 通过直截面矩阵函数, 显示可识别的输入方形矩阵的矩阵, 将显示所有输入方形矩阵的矩阵的矩阵的矩阵的转换状态, 以可识别的矩阵的矩阵函数是可识别的直截式矩阵函数。