  Data-driven modeling of dynamical systems often faces numerous data-related
challenges. A fundamental requirement is the existence of a unique set of
parameters for a chosen model structure, an issue commonly referred to as
identifiability. Although this problem is well studied for ordinary
differential equations (ODEs), few studies have focused on the more general
class of systems described by differential-algebraic equations (DAEs). Examples
of DAEs include dynamical systems with algebraic equations representing
conservation laws or approximating fast dynamics. This work introduces a novel
identifiability test for models characterized by nonlinear DAEs. Unlike
previous approaches, our test only requires prior knowledge of the system
equations and does not need nonlinear transformation, index reduction, or
numerical integration of the DAEs. We employed our identifiability analysis
across a diverse range of DAE models, illustrating how system identifiability
depends on the choices of sensors, experimental conditions, and model
structures. Given the added challenges involved in identifying DAEs when
compared to ODEs, we anticipate that our findings will have broad applicability
and contribute significantly to the development and validation of data-driven
methods for DAEs and other structure-preserving models.
