Algorithm for finding new identifiable reparametrizations of parametric ODEs

Structural identifiability concerns the question of which unknown parameters of a model can be recovered from (perfect) input-output data. If all of the parameters of a model can be recovered from data, the model is said to be identifiable. However, in many models, there are parameters that can take on an infinite number of values but yield the same input-output data. In this case, those parameters and the model are called unidentifiable. The question is then what to do with an unidentifiable model. One can either adjust the model, if experimentally feasible, or try to find a reparametrization to make the model identifiable. In this paper, we take the latter approach. While existing approaches to find identifiable reparametrizations were limited to scaling reparametrizations or were not guaranteed to find an identifiable reparametrization, we show in this paper that there always exists a locally identifiable model with the same input-output behavior as the original one. We also prove that, for linear models, a globally identifiable reparametrization always exists and show that, for a certain class of linear compartmental models, an explicit reparametrization formula exists. We illustrate our method on several examples and provide detailed analysis in supplementary material on github.