Language-based Abstractions for Dynamical Systems

Abstract

Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of effectively performing analyses. This has motivated a large body of research, across many disciplines, into abstraction techniques that provide smaller ODE systems while preserving the original dynamics in some appropriate sense. In this paper we give an overview of a recently proposed computer-science perspective to this problem, where ODE reduction is recast to finding an appropriate equivalence relation over ODE variables, akin to classical models of computation based on labelled transition systems.

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

“…A widely used formalism is that of Markov population models (MPMs), for which ad-hoc algorithms for computing transient distributions [12] and to model check CSL properties [133,34] have been implemented. Enhancing scalability is the main improvement of alternative methods of performance analysis for very large systems, e.g., based on fluid approximation techniques [83,138] and on solving systems of ordinary differential equations (ODEs) [35], which is an approach allowing for producing approximated transient measures for models of 10 100 states and beyond, even thanks to (approximate) reductions [141] and aggregations [139] of ODE systems. These methods are supported by automated analysers, like, e.g., GPA [134], the specification language of which is inspired by a version of the process algebra PEPA, and ERODE [42,141].…”

“…Enhancing scalability is the main improvement of alternative methods of performance analysis for very large systems, e.g., based on fluid approximation techniques [83,138] and on solving systems of ordinary differential equations (ODEs) [35], which is an approach allowing for producing approximated transient measures for models of 10 100 states and beyond, even thanks to (approximate) reductions [141] and aggregations [139] of ODE systems. These methods are supported by automated analysers, like, e.g., GPA [134], the specification language of which is inspired by a version of the process algebra PEPA, and ERODE [42,141]. Approximation methods [15] and scalable reachability analysis techniques [125] are proposed also for mixed models like probabilistic hybrid automata.…”