Paper List

期刊: ArXiv Preprint
发布日期: 2026-03-12
Applied MathematicsSystems Biology

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

Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden | Mathematical Institute, University of Oxford, United Kingdom | School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia | Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden

Johannes G Borgqvist, Alexander P Browning, Fredrik Ohlsson, Ruth E Baker

30秒速读

IN SHORT: This paper addresses the core challenge of systematically determining which parameters and states in a mechanistic ODE model can be uniquely inferred from observed outputs, a fundamental prerequisite for reliable parameter estimation and state reconstruction.

核心创新

  • Methodology Introduces a novel subclass of Lie symmetries, termed 'parameter-state symmetries', which simultaneously transform model parameters and states while preserving all observed outputs at every time point.
  • Theory Proves a fundamental theorem linking locally structurally identifiable parameter combinations and observable states to the universal invariants of all parameter-state symmetries of a model, providing a rigorous mathematical foundation.
  • Methodology Provides a unified framework that simultaneously analyzes local structural identifiability and observability, extending previous work that focused only on identifiability via parameter symmetries of the output system.

主要结论

  • Parameter-state symmetries, defined by their preservation of observed outputs (y(t, x, θ) = y(t, x*, θ*)), provide the precise mathematical objects whose invariants correspond to locally identifiable/observable quantities.
  • The framework successfully recovers known identifiability results (e.g., from differential algebra methods) and reveals new insights into state observability for canonical models like glucose-insulin regulation and SEI epidemiological models.
  • The approach offers a systematic, symmetry-based alternative to established methods (e.g., differential algebra, EAR method) for the joint analysis of two critical structural properties in dynamical systems modeling.
研究空白： Previous methods using 'full symmetries' to analyze local identifiability and observability lacked a clear, formal link between these symmetries and the specific combinations of parameters/states that are identifiable/observable. This work fills that theoretical gap.

摘要: 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.