Identifiability of Differential-Algebraic Systems

TL;DR

This paper presents a new identifiability test for nonlinear differential-algebraic equation (DAE) models that requires only the system equations, aiding model validation and parameter estimation.

Contribution

The work introduces a novel identifiability test for nonlinear DAEs that does not require nonlinear transformations, index reduction, or numerical integration.

Findings

Identifiability depends on sensor placement and experimental conditions.

The test is applicable to a broad class of DAE models.

It simplifies the process of verifying model parameters' uniqueness.

Abstract

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.