eprintid: 3437
rev_number: 7
eprint_status: archive
userid: 69
dir: disk0/00/00/34/37
datestamp: 2016-04-13 08:40:24
lastmod: 2016-04-13 08:40:24
status_changed: 2016-04-13 08:40:24
type: book_section
metadata_visibility: show
creators_name: Cardelli, Luca
creators_name: Tribastone, Mirco
creators_name: Tschaikowski, Max
creators_name: Vandin, Andrea
creators_id: 
creators_id: mirco.tribastone@imtlucca.it
creators_id: max.tschaikowski@imtlucca.it
creators_id: andrea.vandin@imtlucca.it
title: Efficient Syntax-Driven Lumping of Differential Equations
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: public
abstract: 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.
date: 2016
date_type: published
series: Lecture Notes in Computer Science
number: 9636
publisher: Springer
pagerange: 93-111
pages: 18
id_number: 10.1007/978-3-662-49674-9_6
refereed: TRUE
isbn: 978-3-662-49673-2
book_title: Tools and Algorithms for the Construction and Analysis of Systems. 22nd International Conference, TACAS 2016
official_url: http://dx.doi.org/10.1007/978-3-662-49674-9_6
citation:   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)  
document_url: http://eprints.imtlucca.it/3437/1/tacas2016.pdf