Squillace, Giuseppe (2024) Dynamical systems reduction through approximate lumping techniques. Advisor: Tribastone, Prof. Mirco. Coadvisor: Tschaikowski, Prof. Max . pp. 134. [IMT PhD Thesis]
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Text (Doctoral thesis)
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Abstract
Model reduction is a fundamental technique utilized across various disciplines, such as engineering, physics, and compu- tational sciences, to simplify complex mathematical models while retaining essential dynamics. This thesis introduces two novel approaches for model reduc- tion, particularly focusing on dynamical systems described by polynomial ordinary differential equations (ODEs). The pro- posed techniques aim to reduce ODE systems while providing formal error bounds for the resultant reduced models. The first approach, based on backward and forward differen- tial equivalence (BDE/FDE), partitions the set of variables in an ODE system to construct a reduced model, incorporating a tolerance parameter ε to capture perturbations in polynomial coefficients. In the second approach, we present an algorithm to transform an ODE system into a so-called differential hull. This is a construction whereby variables with structurally sim- ilar dynamics but originally different parameters may be rep- resented by the same lower and upper bounds and reduced through the backward differential equivalence. Furthermore, the thesis explores the application of these tech- niques in discovering regular equivalences on networks. An iterative scheme, called iterative ε-BDE, is introduced to com- pute regular equivalences, allowing for the analysis of roles in networks. Experimental evaluations demonstrate the effectiveness and efficiency of the proposed approaches compared to existing methods in the literature.
| Item Type: | IMT PhD Thesis |
|---|---|
| Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
| PhD Course: | Computer science and systems engineering |
| Identification Number: | https://doi.org/10.13118/imtlucca/e-theses/408 |
| NBN Number: | urn:nbn:it:imtlucca-29963 |
| Date Deposited: | 16 Apr 2024 09:21 |
| URI: | http://e-theses.imtlucca.it/id/eprint/408 |
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