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Dynamical systems reduction through approximate lumping techniques

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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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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