Formal lumping of polynomial differential equations through approximate equivalences

Luca Cardelli, Giuseppe Squillace*, Mirco Tribastone, Max Tschaikowski, Andrea Vandin

*Corresponding author for this work

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Abstract

It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem for nonlinear ordinary differential equations (ODEs) with polynomial derivatives. We introduce a model reduction technique based on approximate differential equivalence, i.e., a partition of the set of ODE variables that performs an aggregation when the variables are governed by nearby derivatives. We develop algorithms to (i) compute the largest approximate differential equivalence; (ii) construct an approximately reduced model from the original one via an appropriate perturbation of the coefficients of the polynomials; and (iii) provide a formal certificate on the quality of the approximation as an error bound, computed as an over-approximation of the reachable set of the reduced model. Finally, we apply approximate differential equivalences to case studies on electric circuits, biological models, and polymerization reaction networks.

Original languageEnglish
Article number100876
JournalJournal of Logical and Algebraic Methods in Programming
Volume134
ISSN2352-2208
DOIs
Publication statusPublished - Aug 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Inc.

Keywords

  • Equivalence relations
  • Lumping
  • Model reduction
  • Polynomial differential equations

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