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Finding and breaking Lie symmetries: implications for structural identifiability and observability of dynamic models

Banff International Research Station for Mathematical Innovation and Discovery

A dynamic model is structurally identifiable (respectively, observable) if it is theoretically possible to infer its unknown parameters (respectively, states) by observing its output over time. The two properties, structural identifiability and observability, are completely determined by the model equations. Their analysis is of interest for modellers because it informs about the possibility of gaining insight about the unmeasured variables of a model. Here we cast the problem of analysing structural identifiability and observability as that of finding Lie symmetries. We build on previous results that showed that structural unidentifiability amounts to the existence of Lie symmetries. We consider nonlinear models described by ordinary differential equations and restrict ourselves to rational functions. We revisit a method for finding symmetries by transforming rational expressions into linear systems, and extend it by enabling it to provide symmetry-breaking transformations. This extension allows for a semi-automatic model reformulation that renders a non-observable model observable. We have implemented the methodology in MATLAB, as part of the STRIKE-GOLDD toolbox for observability and identifiability analysis. We illustrate its use in the context of biological modelling by applying it to a set of problems taken from the literature, which also allow us to discuss the implications of (non)observability.

Mathematics; Mathematical logic and foundations; Algebraic geometry

video/mp4

Author affiliation: Consejo Superior de Investigaciones Científicas (CSIC)

2020-12-02

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/76626

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/