Set-based graph methods for fast equation sorting in large DAE systems

Zimmermann, Pablo; Pastor, Joaquı́n; Kofman, Ernesto

doi:10.1145/3365984.3365991

Cited by 5 publications

(8 citation statements)

References 20 publications

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“…In addition, we are also working on developing more algorithms of this type (using SB-Graphs with maps) for other problems related to Modelica compilation: finding maximum matching in bipartite graphs and strongly connected components (directed graphs). These problems were already solved using SB-Graphs in [13] but the solution was quite complicated and not as general as the one found here using maps for representing set-edges. Another related problem that we are trying to solve using SB-Graphs is that of producing the code for computing the sparse Jacobian matrix in large systems of differential algebraic equations.…”

Section: Fundingmentioning

confidence: 93%

“…The algorithms presented in this work are based on the use of Set-Based Graphs (SB-Graphs), first defined in [13]. SB-Graphs are regular graphs in which the vertices and edges are grouped in sets allowing sometimes a compact representation.…”

Section: Set-based Graphsmentioning

confidence: 99%

“…As in regular graphs, we can define bipartite Set-Based Graph and directed Set-Based Graphs. An algortihm for matching in bipartite Set-Based Graph and an algorithm for finding the strongly connected components of a directed Set-based Graph were recently presented in [13].…”

Section: Set-based Graphsmentioning

confidence: 99%

“…The problem of manipulating large graphs grouping vertices and edges into sets to produce compact systems of equations was recently proposed with the introduction of Set-Based Graphs [13]. There, a compact solution for the problems of maximum matching and finding strongly connected components in directed graph for equation sorting was proposed and implemented as part of the prototype ModelicaCC compiler [7].…”

Section: Introductionmentioning

confidence: 99%

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Connected Components in Undirected Set--Based Graphs. Applications in Object--Oriented Model Manipulation

Kofman¹,

Marzorati²,

Fernandez³

2020

Preprint

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This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set-Based Graph. The algorithm, under certain restrictions on those sets, has the remarkable property of achieving constant computational costs with the number of vertices and edges. The mentioned restrictions are related to the possibility of representing the sets of vertices by intension and the sets of edges using some particular type of maps. While these restrictions can result strong in a general context, they are usually satisfied in the problem of transforming connections into equations in object oriented models, which is the main application of the proposed algorithm.Besides describing the new algorithm and studying its computational cost, the work describes its prototype implementation and shows its application in different examples.

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Section: Fundingmentioning

confidence: 93%

Section: Set-based Graphsmentioning

confidence: 99%

Section: Set-based Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Connected Components in Undirected Set--Based Graphs. Applications in Object--Oriented Model Manipulation

Kofman¹,

Marzorati²,

Fernandez³

2020

Preprint

Self Cite

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“…To the best of our knowledge, only (Höger 2015) addresses the specific issue of performing the structural analysis of a hierarchical model; Section 2.1 of this paper shows the approach proposed by Höger and explains why we regard it as an efficient but still partial solution. On the related subject of sorting equations, attention is paid in (Zimmermann, Fernández, and Kofman 2019) to methods that avoid unrolling loops and expanding arrays when sorting equations, an issue targeting the same overall objective as both (Höger 2015;Höger 2019) and the present work.…”

Section: Introductionmentioning

confidence: 99%

Towards the separate compilation of Modelica: modularity and interfaces for the index reduction of incomplete DAE systems

Benveniste,

Caillaud,

Malandain

et al. 2023

Linköping Electronic Conference Proceedings

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A key feature of the Modelica language is its object-oriented nature: components are instances of classes and they can aggregate other components, so that extremely large models can be efficiently designed as ``trees of components''. However, the structural analysis of Modelica models, a necessary step for generating simulation code, often relies on the flattening of this hierarchical structure, which undermines the scalability of the language and results in widely-used Modelica tools not being able to compile and simulate such large models. In this paper, we propose a novel method for the modular structural analysis of Modelica models. An adaptation of Pryce's Sigma-method for non-square DAE systems, along with a carefully crafted notion of component interface, make it possible to fully exploit the object tree structure of a model. The structural analysis of a component class can be performed once and for all, only requiring the information provided by the interface of its child components. The resulting method alleviates the exponential computation costs that can be yielded by model flattening; hence, its scalability makes it ideally suited for the modeling and simulation of large cyber-physical systems.

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Array-Aware Matching: Taming the Complexity of Large-Scale Simulation Models

Fioravanti,

Cattaneo,

Terraneo

et al. 2023

ACM Trans. Math. Softw.

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Equation-based modelling is a powerful approach to tame the complexity of large-scale simulation problems. Equation-based tools automatically translate models into imperative languages. When confronted with nowadays’ problems, however, well assessed model translation techniques exhibit scalability issues, that are particularly severe when models contain very large arrays. In fact, such models can be made very compact by enclosing equations into looping constructs, but reflecting the same compactness into the translated imperative code is not trivial. In this paper, we face this issue by concentrating on a key step of equations-to-code translation, the equation/variable matching. We first show that an efficient translation of models with (large) arrays needs awareness of their presence, by defining a figure of merit to measure how much the looping constructs are preserved along the translation. We then show that the said figure of merit allows to define an optimal array-aware matching, and as our main result, that the so stated optimal array-aware matching problem is NP-complete. As an additional result, we propose a heuristic algorithm capable of performing array-aware matching in polynomial time. The proposed algorithm can be proficiently used by model translator developers in the implementation of efficient tools for large-scale system simulation.

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Set-based graph methods for fast equation sorting in large DAE systems

Cited by 5 publications

References 20 publications

Connected Components in Undirected Set--Based Graphs. Applications in Object--Oriented Model Manipulation

Connected Components in Undirected Set--Based Graphs. Applications in Object--Oriented Model Manipulation

Towards the separate compilation of Modelica: modularity and interfaces for the index reduction of incomplete DAE systems

Array-Aware Matching: Taming the Complexity of Large-Scale Simulation Models

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