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Efficient Syntax-Driven Lumping of Differential Equations

Cardelli, Luca and Tribastone, Mirco and Tschaikowski, Max and Vandin, Andrea Efficient Syntax-Driven Lumping of Differential Equations. In: Tools and Algorithms for the Construction and Analysis of Systems. 22nd International Conference, TACAS 2016. Lecture Notes in Computer Science (9636). Springer, pp. 93-111. ISBN 978-3-662-49673-2 (2016)

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We present an algorithm to compute exact aggregations of a class of systems of ordinary differential equations (ODEs). Our approach consists in an extension of Paige and Tarjan’s seminal solution to the coarsest refinement problem by encoding an ODE system into a suitable discrete-state representation. In particular, we consider a simple extension of the syntax of elementary chemical reaction networks because (i) it can express ODEs with derivatives given by polynomials of degree at most two, which are relevant in many applications in natural sciences and engineering; and (ii) we can build on two recently introduced bisimulations, which yield two complementary notions of ODE lumping. Our algorithm computes the largest bisimulations in O(r⋅s⋅logs)O(r⋅s⋅log⁡s) time, where r is the number of monomials and s is the number of variables in the ODEs. Numerical experiments on real-world models from biochemistry, electrical engineering, and structural mechanics show that our prototype is able to handle ODEs with millions of variables and monomials, providing significant model reductions.

Item Type: Book Section
Identification Number: 10.1007/978-3-662-49674-9_6
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Caterina Tangheroni
Date Deposited: 13 Apr 2016 08:40
Last Modified: 13 Apr 2016 08:40
URI: http://eprints.imtlucca.it/id/eprint/3437

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