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 is knowing if 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 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 equations obtained from the model just using Cramer's rule.
翻译:结构性可识别性是一个差异模型的属性, 其参数允许在没有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, 在实践中经常出现的不同模型类型的输入- 输出方程式系数的可识别性, 例如一个输出型和线形隔间模型的线性模型, 每一个区间都可以达到泄漏或输入。 这显示, 通过这些模型的输入- 输出方程式来检查可识别性是合理的, 正如我们所证明的那样, 可识别功能的字段是由输入- 输出方程式的系数生成的。 最后, 我们证明, 对于一个带有输入和紧密连接的方程式的线形模型, 使用所有可识别的C 方程式的方程式的域, 通过所有可识别的方程式的方程式的域。