Speaker
Description
Parameter fitting workflows, in which model parameter values are recovered from data, are well established in mathematical biology. The introduction of universal differential equations (UDEs) extends this framework by enabling the estimation of not only scalar parameters but also unknown functions. Examples include learning a protein’s production rate as a function of its transcription factor concentration, or an infectious disease’s transmission rate as a function of the number of infected individuals. Within parameter fitting, the identifiability concept describes our ability to recover true parameter values from data. That is, identifiability analysis determines whether alternative parameter sets can produce equally good fits to observations. The absence of such alternatives suggests that the inferred parameters reflect the true system dynamics.
Here, we extend the concept of identifiability from scalar parameters to unknown functions. We demonstrate how to assess both structural functional identifiability (i.e. whether a function is fundamentally recoverable, even with perfect data) and practical functional identifiability (i.e. whether a function is recoverable given available data). In both cases, we show how to handle additional sources of nuisance that are not present for standard parametric identifiability. Finally, we show that UDE identifiability can be decomposed into parametric and functional components (with the parametric component assessable using classical parameter identifiability methods) together yielding a complete characterisation of UDE identifiability.
