Language-based Abstractions for Dynamical Systems

TL;DR

This paper reviews a computer science approach to simplifying complex dynamical systems modeled by ODEs through abstractions that preserve their core behavior, enabling more efficient analysis.

Contribution

It introduces a novel perspective on ODE reduction by framing it as finding equivalence relations over variables, inspired by models of computation.

Findings

Provides an overview of a new abstraction technique for ODEs

Shows how equivalence relations can simplify dynamical system models

Connects ODE reduction to classical computational models

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.