Language-based Abstractions for Dynamical Systems

@inproceedings{Vandin2017LanguagebasedAF,
  title={Language-based Abstractions for Dynamical Systems},
  author={Andrea Vandin},
  booktitle={QAPL@ETAPS},
  year={2017}
}
  • Andrea Vandin
  • Published in QAPL@ETAPS 13 July 2017
  • Computer Science
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… 

Figures from this paper

Quantitative Aspects of Programming Languages and Systems over the past $2^4$ years and beyond
TLDR
The aim of this survey is to revisit such achievements and results from the standpoint of QAPL and its community.

References

SHOWING 1-10 OF 66 REFERENCES
Symbolic computation of differential equivalences
TLDR
This work proposes differential equivalence relations for biochemical models from the literature that cannot be reduced using competing automatic techniques, and provides novel symbolic procedures to check an equivalence and compute the largest one via partition refinement algorithms that use satisfiability modulo theories.
Efficient Syntax-Driven Lumping of Differential Equations
TLDR
Numerical experiments on real-world models from biochemistry, electrical engineering, and structural mechanics show that the prototype is able to handle ODEs with millions of variables and monomials, providing significant model reductions.
Differential Bisimulation for a Markovian Process Algebra
TLDR
This work presents differential bisimulation, a behavioral equivalence developed as the ODE counterpart of bisimulations for languages with probabilistic or stochastic semantics, and provides an efficient partition-refinement algorithm to compute the coarsest ODE aggregation of a model according to differential bisIMulation.
Stochastic Process Algebras: From Individuals to Populations
TLDR
It is shown how population-based models that make use of a continuous approximation of the discrete behaviour can be used to efficiently analyse the temporal behaviour of very large systems via their collective dynamics.
The Continuous pi-Calculus: A Process Algebra for Biochemical Modelling
TLDR
The continuous π-calculus, a process algebra for modelling behaviour and variation in molecular systems, is introduced and its expressive succinctness and support for diverse interaction between agents via a flexible network of molecular affinities are discussed.
ERODE: A Tool for the Evaluation and Reduction of Ordinary Differential Equations
TLDR
ERODE supports two recently introduced, complementary, equivalence relations over ODE variables: forward differential equivalence yields a self-consistent aggregate system where each ODE gives the cumulative dynamics of the sum of the original variables in the respective equivalence class.
Quantitative Abstractions for Collective Adaptive Systems
TLDR
This chapter treats the problem of efficiently analysing large-scale CAS for quantitative properties and reviews algorithms to automatically reduce the dimensionality of a CAS model preserving modeller-defined state variables, with focus on descriptions based on systems of ordinary differential equations.
Comparing Chemical Reaction Networks: A Categorical and Algorithmic Perspective
TLDR
This work uses a categorical framework to extend and relate model-comparison approaches based on structural and dynamical properties of a CRN to prove their equivalence, and provides an algorithm to compare CRNs, running linearly in time with respect to the cardinality of all possible comparisons.
Quantitative Relations and Approximate Process Equivalences
TLDR
A characterisation of probabilistic transition systems (PTS) in terms of linear operators on some suitably defined vector space representing the set of states is introduced and it is argued that this number can be given a statistical interpretation in Terms of the tests needed to distinguish two behaviours.
Exact fluid lumpability in Markovian process algebra
...
...