TY - JOUR
T1 - Formal lumping of polynomial differential equations through approximate equivalences
AU - Cardelli, Luca
AU - Squillace, Giuseppe
AU - Tribastone, Mirco
AU - Tschaikowski, Max
AU - Vandin, Andrea
N1 - Publisher Copyright:
© 2023 Elsevier Inc.
PY - 2023/8
Y1 - 2023/8
N2 - 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.
AB - 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.
KW - Equivalence relations
KW - Lumping
KW - Model reduction
KW - Polynomial differential equations
UR - http://www.scopus.com/inward/record.url?scp=85162810920&partnerID=8YFLogxK
U2 - 10.1016/j.jlamp.2023.100876
DO - 10.1016/j.jlamp.2023.100876
M3 - Journal article
AN - SCOPUS:85162810920
SN - 2352-2208
VL - 134
JO - Journal of Logical and Algebraic Methods in Programming
JF - Journal of Logical and Algebraic Methods in Programming
M1 - 100876
ER -