Robust global identifiability theory using potentials—Application to compartmental models

• A new global identifiability theory using potentials presented.
• Method provides both a theory for global identifiability and a direct method for system identification.
• System identification method does not require any simulations of the underlying model so is very computationally efficient.
• Approach is robust to noise, allows for iteration as required, and applicable to multiple experiments with heteroscedastic noise.
• Provides the theoretical basis for an integral method used extensively in critical care.

This paper presents a global practical identifiability theory for analyzing and identifying linear and nonlinear compartmental models. The compartmental system is prolonged onto the potential jet space to formulate a set of input–output equations that are integrals in terms of the measured data, which allows for robust identification of parameters without requiring any simulation of the model differential equations. Two classes of linear and non-linear compartmental models are considered. The theory is first applied to analyze the linear nitrous oxide (N2O) uptake model. The fitting accuracy of the identified models from differential jet space and potential jet space identifiability theories is compared with a realistic noise level of 3% which is derived from sensor noise data in the literature. The potential jet space approach gave a match that was well within the coefficient of variation. The differential jet space formulation was unstable and not suitable for parameter identification. The proposed theory is then applied to a nonlinear immunological model for mastitis in cows. In addition, the model formulation is extended to include an iterative method which allows initial conditions to be accurately identified. With up to 10% noise, the potential jet space theory predicts the normalized population concentration infected with pathogens, to within 9% of the true curve.