# Efficient Syntax-Driven Lumping of Differential Equations

@inproceedings{Cardelli2016EfficientSL, title={Efficient Syntax-Driven Lumping of Differential Equations}, author={Luca Cardelli and Mirco Tribastone and Max Tschaikowski and Andrea Vandin}, booktitle={TACAS}, year={2016} }

We present an algorithm to compute exact aggregations of a class of systems of ordinary differential equations ODEs. Our approach consists in an extension of Paige and Tarjan's seminal solution to the coarsest refinement problem by encoding an ODE system into a suitable discrete-state representation. In particular, we consider a simple extension of the syntax of elementary chemical reaction networks because i it can express ODEs with derivatives given by polynomials of degree at most two, which…

## 25 Citations

Symbolic computation of differential equivalences

- Computer SciencePOPL
- 2016

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.

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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.

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An aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion).

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An overview of a recently proposed computer-science perspective to ODE reduction is recast to finding an appropriate equivalence relation over ODE variables, akin to classical models of computation based on labelled transition systems.

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- 2017

An efficient partition-refinement algorithm which computes the largest SMB of a CRN in polynomial time in the number of species and reactions, and implies forward CRN bisimulation, a recently developed behavioral notion of equivalence for the ODE semantics, in an analogous sense: it yields a smaller ODE system that keeps track of the sums of the solutions for equivalent species.

Backward Invariance for Linear Differential Algebraic Equations

- Mathematics2018 IEEE Conference on Decision and Control (CDC)
- 2018

Backward invariance is presented, which relates DAE variables that have equal solutions at all time points (thus requiring them to start with equal initial conditions), and applied to the electrical engineering domain, showing that backward invariance can explain symmetries in certain networks as well as analyze DAEs which could not be originally treated due to their size.

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- Computer Science2018 Winter Simulation Conference (WSC)
- 2018

This paper offers an advanced tutorial on an array of recently developed algorithms that seek to tame the complexity of these models by aggregating their constituting systems of equations, leading to lower-dimensional systems that preserve the original dynamics in some appropriate, formal sense.

SPEEDING UP STOCHASTIC AND DETERMINISTIC SIMULATION BY AGGREGATION: AN ADVANCED TUTORIAL

- Computer Science
- 2018

This paper offers an advanced tutorial on an array of recently developed algorithms that seek to tame the complexity of these models by aggregating their constituting systems of equations, leading to lower-dimensional systems that preserve the original dynamics in some appropriate, formal sense.

A large-scale assessment of exact lumping of quantitative models in the BioModels repository

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