1 research outputs found
Computing all identifiable functions of parameters 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. However, this solvability condition is not always satisfied, which
presents a challenge. Our first main result is an algorithm that computes all
identifiable functions without any additional assumptions, which is the first
such algorithm as far as we know. Our second main result concerns the
identifiability from multiple experiments (with generically different inputs
and initial conditions among the experiments). For this problem, we prove that
the set of functions identifiable from multiple experiments is what would
actually be computed by input-output equation-based algorithms (whether or not
the solvability condition is fulfilled), which was not known before. 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