TY - GEN

T1 - An Algorithm for the Formal Reduction of Differential Equations as Over-Approximations

AU - Squillace, Giuseppe

AU - Tribastone, Mirco

AU - Tschaikowski, Max

AU - Vandin, Andrea

N1 - Publisher Copyright:
© 2022, Springer Nature Switzerland AG.

PY - 2022

Y1 - 2022

N2 - Models of complex systems often consist of state variables with structurally similar dynamics that differ in the specific values of some parameters. Examples are multi-class epidemiological models, chemical reaction networks describing multiple components (e.g., binding sites) with equivalent functional behavior, and models of electric circuits with replicated designs. In these cases, the analysis may be expensive due to the model size. Here we consider models defined as systems of polynomial ordinary differential equations (ODEs) with positive solutions. We present an algorithm to reduce the computational cost by transforming the original ODE model into one for which we can compute an appropriate over-approximation on a smaller set of state variables. The algorithm is based on the theory of differential inequalities and consists of two steps. The first step computes a differential hull, which is an ODE system providing lower and upper bounds for each state variable. The hull is constructed such that variables with structurally similar dynamics but originally different parameters may now be represented by the same lower and upper bounds. Based on this, the second step exploits already developed notions of exact model reduction for ODEs to lump such variables. The algorithm is showcased on several case studies and its results are favourably compared against CORA, a well-known tool for reachability analysis of dynamical systems.

AB - Models of complex systems often consist of state variables with structurally similar dynamics that differ in the specific values of some parameters. Examples are multi-class epidemiological models, chemical reaction networks describing multiple components (e.g., binding sites) with equivalent functional behavior, and models of electric circuits with replicated designs. In these cases, the analysis may be expensive due to the model size. Here we consider models defined as systems of polynomial ordinary differential equations (ODEs) with positive solutions. We present an algorithm to reduce the computational cost by transforming the original ODE model into one for which we can compute an appropriate over-approximation on a smaller set of state variables. The algorithm is based on the theory of differential inequalities and consists of two steps. The first step computes a differential hull, which is an ODE system providing lower and upper bounds for each state variable. The hull is constructed such that variables with structurally similar dynamics but originally different parameters may now be represented by the same lower and upper bounds. Based on this, the second step exploits already developed notions of exact model reduction for ODEs to lump such variables. The algorithm is showcased on several case studies and its results are favourably compared against CORA, a well-known tool for reachability analysis of dynamical systems.

KW - Model reduction

KW - Ordinary differential equations

KW - Reachability analysis

U2 - 10.1007/978-3-031-16336-4_9

DO - 10.1007/978-3-031-16336-4_9

M3 - Article in proceedings

AN - SCOPUS:85138995820

SN - 9783031163357

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 173

EP - 191

BT - Proceedings of 19th International Conference on Quantitative Evaluation of Systems

A2 - Ábrahám, Erika

A2 - Paolieri, Marco

PB - Springer

T2 - 19<sup>th</sup> International Conference on Quantitative Evaluation of Systems

Y2 - 12 September 2022 through 16 September 2022

ER -