Framing local structural identifiability and observability in terms of parameter-state symmetries

TL;DR

This paper introduces parameter-state symmetries to analyze local structural identifiability and observability in mechanistic models, providing a unified symmetry-based framework that confirms and extends previous results.

Contribution

The paper defines a new class of Lie symmetries called parameter-state symmetries and links them to identifiability and observability in state-dependent ODE models.

Findings

Confirmed known identifiability results on four models.

Revealed new insights into state observability.

Provided a unified symmetry-based analysis framework.

Abstract

We introduce a subclass of Lie symmetries, called parameter-state symmetries, to analyse the local structural identifiability and observability of mechanistic models consisting of state-dependent ODEs with observed outputs. These symmetries act on parameters and states while preserving observed outputs at every time point. We prove that locally structurally identifiable parameter combinations and locally structurally observable states correspond to universal invariants of all parameter-state symmetries of a given model. We illustrate the framework on four previously studied mechanistic models, confirming known identifiability results and revealing novel insights into which states are observable, providing a unified symmetry-based approach for analysing structural properties of dynamical systems.