Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological Modelling
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 e...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/3/469 |
| _version_ | 1818035569768267776 |
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| author | Gemma Massonis Alejandro F. Villaverde |
| author_facet | Gemma Massonis Alejandro F. Villaverde |
| author_sort | Gemma Massonis |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T06:57:09Z |
| format | Article |
| id | doaj.art-075a9a9a0e6046eeaf2ec97de76d74e5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-12-10T06:57:09Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-075a9a9a0e6046eeaf2ec97de76d74e52022-12-22T01:58:24ZengMDPI AGSymmetry2073-89942020-03-0112346910.3390/sym12030469sym12030469Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological ModellingGemma Massonis0Alejandro F. Villaverde1BioProcess Engineering Group, IIM-CSIC, 36208 Vigo, Galicia, SpainBioProcess Engineering Group, IIM-CSIC, 36208 Vigo, Galicia, SpainA 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.https://www.mdpi.com/2073-8994/12/3/469dynamic modellingnonlinear systemsobservabilitystructural identifiabilitylie symmetries |
| spellingShingle | Gemma Massonis Alejandro F. Villaverde Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological Modelling Symmetry dynamic modelling nonlinear systems observability structural identifiability lie symmetries |
| title | Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological Modelling |
| title_full | Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological Modelling |
| title_fullStr | Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological Modelling |
| title_full_unstemmed | Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological Modelling |
| title_short | Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological Modelling |
| title_sort | finding and breaking lie symmetries implications for structural identifiability and observability in biological modelling |
| topic | dynamic modelling nonlinear systems observability structural identifiability lie symmetries |
| url | https://www.mdpi.com/2073-8994/12/3/469 |
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