Parameter Estimation in ODE Models with Certified Polynomial System Solving
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915256495767552 |
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| author | Demin, Alexander Ovchinnikov, Alexey Rouillier, Fabrice |
| author_facet | Demin, Alexander Ovchinnikov, Alexey Rouillier, Fabrice |
| contents | We consider dynamical models given by rational ODE systems. Parameter estimation is an important and challenging task of recovering parameter values from observed data. Recently, a method based on differential algebra and rational interpolation was proposed to express parameter estimation in terms of polynomial system solving. Typically, polynomial system solving is a bottleneck, hence the choice of the polynomial solver is crucial. In this contribution, we compare two polynomial system solvers applied to parameter estimation: homotopy continuation solver from HomotopyContinuation.jl and our new implementation of a certified solver based on rational univariate representation (RUR) and real root isolation. We show how the new RUR solver can tackle examples that are out of reach for the homotopy methods and vice versa. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_17268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parameter Estimation in ODE Models with Certified Polynomial System Solving Demin, Alexander Ovchinnikov, Alexey Rouillier, Fabrice Symbolic Computation Mathematical Software Systems and Control Dynamical Systems 68W30, 34-04, 93B30 We consider dynamical models given by rational ODE systems. Parameter estimation is an important and challenging task of recovering parameter values from observed data. Recently, a method based on differential algebra and rational interpolation was proposed to express parameter estimation in terms of polynomial system solving. Typically, polynomial system solving is a bottleneck, hence the choice of the polynomial solver is crucial. In this contribution, we compare two polynomial system solvers applied to parameter estimation: homotopy continuation solver from HomotopyContinuation.jl and our new implementation of a certified solver based on rational univariate representation (RUR) and real root isolation. We show how the new RUR solver can tackle examples that are out of reach for the homotopy methods and vice versa. |
| title | Parameter Estimation in ODE Models with Certified Polynomial System Solving |
| topic | Symbolic Computation Mathematical Software Systems and Control Dynamical Systems 68W30, 34-04, 93B30 |
| url | https://arxiv.org/abs/2504.17268 |