Efficient Syntax-Driven Lumping of Differential Equations

  • Luca CardelliEmail author
  • Mirco TribastoneEmail author
  • Max TschaikowskiEmail author
  • Andrea VandinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9636)


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 \(O(r \cdot s \cdot \log s)\) 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.


Satisfiability Modulo Theory Initial Partition Unary Reaction Partition Block Binary Reaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was partially supported by the EU project QUANTICOL, 600708. L. Cardelli is partially funded by a Royal Society Research Professorship.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Microsoft ResearchCambridgeUK
  2. 2.University of OxfordOxfordUK
  3. 3.IMT Institute for Advanced Studies LuccaLuccaItaly

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