Symmetry-Based Structural Identifiability and Observability Analysis of PDE and ODE Models

Abstract

Structural identifiability and observability are properties that describe the ability to determine the parameters and states of a model from knowledge of its equations, inputs, and outputs. A model is structurally unidentifiable if different parameter sets produce identical outputs. This issue may arise in partially observed systems. In this work, we follow an approach, to which we refer as the SIM algorithm, to analyse identifiability and observability in dynamical systems based on finding its scaling symmetries. The proposed method relies on analysing the invariance of the system under parameter and state scaling transformations and can be systematically applied regardless of the model’s dimensionality. We report the implementation of the SIM method for ODE models in the STRIKE-GOLDD MATLAB toolbox, and extend it to partial differential equation (PDE) models through the newly introduced SIM-PDE algorithm. The approach is straightforward to implement and computationally efficient, making it suitable even for highly nonlinear and large-scale models.