Computing all identifiable functions for ODE models

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. We provide an implementation of the presented algorithms.