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Open AccessArticle

Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological Modelling

BioProcess Engineering Group, IIM-CSIC, 36208 Vigo, Galicia, Spain
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Symmetry 2020, 12(3), 469; https://doi.org/10.3390/sym12030469
Received: 27 February 2020 / Revised: 13 March 2020 / Accepted: 14 March 2020 / Published: 16 March 2020
(This article belongs to the Special Issue Lie Symmetries at Work in Biology and Medicine)
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 into a model’s unmeasured variables. 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. We extend the method by enabling it to provide symmetry-breaking transformations, which allows for a semi-automatic model reformulation that renders a non-observable model observable. We provide a MATLAB implementation of the methodology as part of the STRIKE-GOLDD toolbox for observability and identifiability analysis. We illustrate the use of the methodology in the context of biological modelling by applying it to a set of problems taken from the literature. View Full-Text
Keywords: dynamic modelling; nonlinear systems; observability; structural identifiability; Lie symmetries dynamic modelling; nonlinear systems; observability; structural identifiability; Lie symmetries
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Massonis, G.; Villaverde, A.F. Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological Modelling. Symmetry 2020, 12, 469.

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