Algebraic identifiability of partial differential equation models
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929235265847296 |
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| author | Byrne, Helen Harrington, Heather Ovchinnikov, Alexey Pogudin, Gleb Rahkooy, Hamid Soto, Pedro |
| author_facet | Byrne, Helen Harrington, Heather Ovchinnikov, Alexey Pogudin, Gleb Rahkooy, Hamid Soto, Pedro |
| contents | Differential equation models are crucial to scientific processes. The values of model parameters are important for analyzing the behaviour of solutions. A parameter is called globally identifiable if its value can be uniquely determined from the input and output functions. To determine if a parameter estimation problem is well-posed for a given model, one must check if the model parameters are globally identifiable. This problem has been intensively studied for ordinary differential equation models, with theory and several efficient algorithms and software packages developed. A comprehensive theory of algebraic identifiability for PDEs has hitherto not been developed due to the complexity of initial and boundary conditions. Here, we provide theory and algorithms, based on differential algebra, for testing identifiability of polynomial PDE models. We showcase this approach on PDE models arising in the sciences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04241 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic identifiability of partial differential equation models Byrne, Helen Harrington, Heather Ovchinnikov, Alexey Pogudin, Gleb Rahkooy, Hamid Soto, Pedro Quantitative Methods Symbolic Computation Systems and Control Analysis of PDEs 92B05, 12H05, 35R30, 93C20, 93B25, 93B30 Differential equation models are crucial to scientific processes. The values of model parameters are important for analyzing the behaviour of solutions. A parameter is called globally identifiable if its value can be uniquely determined from the input and output functions. To determine if a parameter estimation problem is well-posed for a given model, one must check if the model parameters are globally identifiable. This problem has been intensively studied for ordinary differential equation models, with theory and several efficient algorithms and software packages developed. A comprehensive theory of algebraic identifiability for PDEs has hitherto not been developed due to the complexity of initial and boundary conditions. Here, we provide theory and algorithms, based on differential algebra, for testing identifiability of polynomial PDE models. We showcase this approach on PDE models arising in the sciences. |
| title | Algebraic identifiability of partial differential equation models |
| topic | Quantitative Methods Symbolic Computation Systems and Control Analysis of PDEs 92B05, 12H05, 35R30, 93C20, 93B25, 93B30 |
| url | https://arxiv.org/abs/2402.04241 |