https://orcid.org/0009-0005-6571-1959
Abstract
This article describes the theory behind constraint hypergraphs: a novel modeling framework that can be used to universally represent and simulate complex systems. Multi-domain system models are traditionally compiled from many diverse frameworks, each based on a single domain. Incompatibilities between these frameworks prevent information from being shared resulting in data silos, duplicate work, and knowledge gaps. A constraint hypergraph addresses these problems by providing a universal modeling framework within which all model prescriptions can be expressed. This methodology expands mathematical structures previously explored in the abstract mathematics and systems theory into a new executable framework. Each hypergraph expresses the holistic behavior of a system in a declarative paradigm that describes the relationships between system properties. In addition to modeling, it is shown how constraint hypergraphs can be used for universal, cross-cutting simulation through principles of function composition. The theoretical framework of a constraint hypergraph is demonstrated with a practical representation of a hybrid system, combining a discrete-event simulation and continuous proportional-integral-derivative controller into a single model of an elevator lift system.
References
1.
Boulding
, K.
, 1956
, “General Systems Theory: The Skeleton of Science
,” Manage. Sci.
, 2
(3
), pp. 197
–208
. 2.
Friedenthal
, S.
, Moore
, A.
, and Steiner
, R.
, 2015
, A Practical Guide to SysML : The Systems Modeling Language
, 3rd ed., Elsevier
, Waltham, MA
.3.
Modelica Association
, 2000
, “Modelica – A Unified Object-Oriented Language for Physical Systems Modeling.”4.
Larsson
, J.
, 2003
, “Interoperability in Modeling and Simulation,” Ph.D. thesis, Linköpings Universitet, Linköping, Sweden.5.
Willems
, J. C.
, 2007
, “The Behavioral Approach to Open and Interconnected Systems
,” IEEE Control Syst. Magaz.
, 27
(6
), pp. 46
–99
. 6.
Hudak
, P.
, 1989
, “Conception, Evolution, and Application of Functional Programming Languages
,” ACM Comput. Surv.
, 21
(3
), pp. 359
–411
. 7.
Rossi
, F.
, van Beek
, P.
, and Walsh
, T.
, 2008
, “Constraint Programming,” Foundations of Artificial Intelligence
, Vol. 3
, F.
van Harmelen
, V.
Lifschitz
, and B.
Porter
, eds., Elsevier
, Amsterdam
, pp. 181
–211
. 8.
Kschischang
, F.
, Frey
, B.
, and Loeliger
, H.-A.
, 2001
, “Factor Graphs and the Sum-Product Algorithm
,” IEEE Trans. Inform. Theory
, 47
(2
), pp. 498
–519
. 9.
Loeliger
, H.-A.
, 2004
, “An Introduction to Factor Graphs
,” IEEE Signal Process. Magaz.
, 21
(1
), pp. 28
–41
. 10.
MacLennan
, B. J.
, 1990
, Functional Programming: Practice and Theory
, Addison-Wesley
, Reading, MA
.11.
International Organization for Standardization
, 2023
, “Systems and Software Engineering – System Life Cycle Processes”.12.
Lee
, E. A.
, 2021
, “Determinism
,” ACM Trans. Embed. Comput. Syst.
, 20
(5
), pp. 38:1
–38:34
. 13.
Willems
, J. C.
, 1989
, “Models for Dynamics”. In Dynamics Reported
, U.
Krichgraber
and H. O.
Walther
and B. G.
Teubner
, eds., Vol. 2
. John Wiley & Sons Ltd
., pp. 171
–266
.14.
Hauser
, R. M.
, and Warren
, J. R.
, 1997
, “Socioeconomic Indexes for Occupations: A Review, Update, and Critique
,” Soc. Methodol.
, 27
(1
), pp. 177
–298
. 15.
Lotka
, A. J.
, 1920
, “Analytical Note on Certain Rhythmic Relations in Organic Systems
,” Proc. Natl. Acad. Sci. U S A
, 6
(7
), pp. 410
–415
. 16.
Ouliaris
, S.
, 2012
, “Economic Models: Simulations of Reality”.17.
Fong
, B.
, and Spivak
, D. I.
, 2018
, “Seven Sketches in Compositionality: An Invitation to Applied Category Theory”.18.
Fong
, B.
, 2016
, “The Algebra of Open and Interconnected Systems,” Ph.D thesis
, Oxford University
, Oxford, UK
. 19.
Baez
, J. C.
, and Pollard
, B. S.
, 2017
, “A Compositional Framework for Reaction Networks
,” Rev. Math. Phys.
, 29
(9
), p. 1750028
. 20.
Patterson
, E.
, Spivak
, D. I.
, and Vagner
, D.
, 2021
, “Wiring Diagrams as Normal Forms for Computing in Symmetric Monoidal Categories
,” 3rd Annual International Applied Category Theory Conference (ACT 2020)
, Cambridge, MA
.21.
Patterson
, E.
, Baas
, A.
, Hosgood
, T.
, and Fairbanks
, J.
, 2022
, “A Diagrammatic View of Differential Equations in Physics
,” MINE
, 5
(2
), pp. 1
–59
. 22.
Mac Lane
, S.
, 1971
, Categories for the Working Mathematician. No. 5 in Graduate Texts in Mathematics. Springer-Verlag, New York.23.
Palm
, W. J.
, 2014
, “Block Diagrams, State-Variable Models, and Simulation Methods”. In System Dynamics
, 3rd ed., McGraw-Hill Science
, New York, NY
, pp. 250
–318
.24.
Borutzky
, W.
, 2011
, Bond Graph Modelling of Engineering Systems: Theory, Applications and Software Support
, Springer
, New York, NY
.25.
Paytner
, H. M.
, 2000
, “The Gestation and Birth of Bond Graphs”.26.
McPhee
, J. J.
, 1996
, “On the Use of Linear Graph Theory in Multibody System Dynamics
,” Nonlinear Dyn.
, 9
(1
), pp. 73
–90
. 27.
Trent
, H. M.
, 1955
, “Isomorphisms Between Oriented Linear Graphs and Lumped Physical Systems
,” J. Acoust. Soc. Am.
, 27
(3
), pp. 500
–527
. 28.
Fisher
, I.
, 1896
, “What is Capital?
” Econ. J.
, 6
(24
), pp. 509
–534
. 29.
Baez
, J.
, Li
, X.
, Libkind
, S.
, Osgood
, N. D.
, and Patterson
, E.
, 2023
, “Compositional Modeling With Stock and Flow Diagrams
,” Fifth International Conference on Applied Category Theory (ACT2023)
, Glasgow, UK
. 30.
Chen
, P. P.-S.
, 1976
, “The Entity-Relationship Model—Toward a Unified View of Data
,” ACM Trans. Database Syst.
, 1
(1
), pp. 9
–36
. 31.
Gilbreth
, F. B.
, and Gilbreth
, L. M.
, 1921
, “Process Charts,” In Annual Meeting of The American Society of Mechanical Engineers, American Society of Mechanical Engineers.32.
Ibe
, O. C.
, 2013
, Markov Processes for Stochastic Modeling, 2nd ed., Elsevier Insights. Elsevier, London.33.
Daly
, R.
, Shen
, Q.
, and Aitken
, S.
, 2011
, “Learning Bayesian Networks: Approaches and Issues
,” Knowl. Eng. Rev.
, 26
(2
), pp. 99
–157
. 34.
Pearl
, J.
, 2009
, Causality
, Cambridge University Press
, Cambridge
.35.
Paredis
, C.
, Diaz-Calderon
, A.
, Sinha
, R.
, and Khosla
, P.
, 2001
, “Composable Models for Simulation-Based Design
,” EWC
, 17
(2
), pp. 112
–128
. 36.
Peak
, R.
, Paredis
, C.
, Tamburini
, D.
, and Waterbury
, S.
, 2005
, “The Composable Object (COB) Knowledge Representation: Enabling Advanced Collaborative Engineering Environments (CEEs),” Technical Report, National Aeronautics and Space Administration.37.
Object Modeling Group
, 2007
, OMG Systems Modeling Language (OMG SysML).38.
Friedman
, G. J.
, and Leondes
, C. T.
, 1969
, “Constraint Theory, Part I: Fundamentals
,” IEEE Trans. Syst. Sci. Cyber.
, 5
(1
), pp. 48
–56
. 39.
Dechter
, R.
, 1992
, “Constraint Networks”. In Encyclopedia of Artificial Intelligence
, S. C.
Shapiro
, ed., 2nd ed., Vol. 1
, John Wiley & Sons Inc
., New York
, pp. 276
–285
.40.
Lecoutre
, C.
, 2013
, Constraint Networks: Targeting Simplicity for Techniques and Algorithms
, John Wiley & Sons
, Hoboken, NJ
.41.
Sinha
, R.
, Paredis
, C. J. J.
, Liang
, V.-C.
, and Khosla
, P. K.
, 2001
, “Modeling and Simulation Methods for Design of Engineering Systems
,” ASME J. Comput. Inf. Sci. Eng
, 1
(1
), pp. 84
–91
. 42.
Morris
, J.
, Mocko
, G.
, and Wagner
, J.
, 2025
, “Effects of Functional and Declarative Modeling Frameworks on System Simulation”. [Manuscript submitted for review to the ASME Journal of Dynamic Systems, Measurement and Control].43.
Andersson
, C.
, 2016
, “Methods and Tools for Co-Simulation of Dynamic Systems With the Functional Mock-Up Interface
,” Doctoral Dissertation in Mathematical Sciences, Lund University
, Lund, Sweden
.44.
de Vries
, T. J. A.
, Weustink
, P. B. T.
, and Cremer
, J. A.
, 1997
, “Improving Dynamic System Model Building Through Constraints
,” Lancaster International Workshop on Engineering Design CACD'97
, Lancaster
.45.
Feldkamp
, F.
, Heinrich
, M.
, and Meyer-Gramann
, K. D.
, 1998
, “SyDeR—System Design for Reusability
,” AIEDAM
, 12
(4
), pp. 373
–382
. 46.
Blochwitz
, T.
, Otter
, M.
, Arnold
, M.
, Bausch
, C.
, Clauß
, C.
, Elmqvist
, H.
, Junghanns
, A.
, Mauss
, J.
, Monteiro
, M.
, Neidhold
, T.
, Neumerkel
, D.
, Olsson
, H.
, Peetz
, J.-V.
, and Wolf
, S.
, 2011
, “The Functional Mockup Interface for Tool Independent Exchange of Simulation Models
,” 8th International Modelica Conference
, Dresden, Germany
.47.
Broman
, D.
, Greenberg
, L.
, Lee
, E. A.
, Masin
, M.
, Tripakis
, S.
, and Wetter
, M.
, 2015
, “Requirements for Hybrid Cosimulation Standards
,” Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control, HSCC ’15, Association for Computing Machinery
, pp. 179
–188
.48.
Wolny
, S.
, Mazak
, A.
, Carpella
, C.
, Geist
, V.
, and Wimmer
, M.
, 2020
, “Thirteen Years of SysML: A Systematic Mapping Study
,” Softw. Syst. Model
, 19
(1
), pp. 111
–169
. 49.
Harel
, D.
, and Pnueli
, A.
, 1985
, “Reactive Systems,” In Logics and Models of Concurrent Systems
, K.
Apt
, ed., Vol. 13 of NATO ASI Series
, Springer
.50.
Friedman
, G. J.
, and Phan
, P.
, 2017
, Constraint Theory, Vol. 23 of IFSR International Series on Systems Science and Engineering, Springer International Publishing, Cham.51.
Gomes
, C.
, Thule
, C.
, Broman
, D.
, Larsen
, P. G.
, and Vangheluwe
, H.
, 2018
, “Co-Simulation: A Survey
,” ACM Comput. Surv.
, 51
(3
), pp. 49:1
–49:39
. 52.
Berge
, C.
, 1973
, Graphs and Hypergraphs, Vol. 6 of North-Holland Mathematical Library, Vol. 6. North-Holland Pub. Co., American Elsevier Pub. Co, Amsterdam, New York.53.
Herstein
, I. N.
, 1964
, Topics in Algebra
, 1st ed., Blaisdell Publishing Company
, Waltham, MA
.54.
Ausiello
, G.
, Giaccio
, R.
, Italiano
, G.
, and Nanni
, U.
, 1992
, “Optimal Traversal of Directed Hypergraphs. ICSI Technical Report ICSI TR-92-073,” International Computer Science Institute, Berkeley, CA.55.
Ausiello
, G.
, and Laura
, L.
, 2017
, “Directed Hypergraphs: Introduction and Fundamental Algorithms—A Survey
,” Theor. Comput. Sci.
, 658
(Part B
), pp. 293
–306
. 56.
Diestel
, R.
, 2017
, Graph Theory
, Vol. 173
, Springer
, Berlin
. 57.
Wymore
, A. W.
, 1993
, Model-Based Systems Engineering: An Introduction to the Mathematical Theory of Discrete Systems and to the Tricotyledon Theory of System Design. Systems Engineering Series. CRC Press, Boca Raton, FL.58.
Rossi
, F.
, van Beek
, P.
, and Walsh
, T.
, 2007
, Handbook of Constraint Programming. Foundations of Artificial Intelligence. Elsevier, Amsterdam Heidelberg.59.
Gomes
, C.
, Meyers
, B.
, Denil
, J.
, Thule
, C.
, Lausdahl
, K.
, Vangheluwe
, H.
, and De Meulenaere
, P.
, 2019
, “Semantic Adaptation for FMI Co-Simulation With Hierarchical Simulators
,” Simulation
, 95
(3
), pp. 241
–269
. 60.
Wolf
, C.
, Schleipen
, M.
, and Frey
, G.
, 2023
, “Secure Exchange of Black-Box Simulation Models Using FMI in the Industrial Context
,” The 15th International Modelica Conference
, Aachen, Germany
, pp. 487
–496
..61.
Morris
, J.
, 2024
, “Constraint Hg”.62.
Moigne
, J. L.
, and Smith
, B.
, 2022
, “Advanced Information Systems Technology (AIST) Earth Systems Digital Twin (ESDT) Workshop Report,” Technical Report, NASA.63.
Walters
, A.
, 2019
, “National Digital Twin Programme”.64.
Walker
, A.
, 2023
, “Singapore’s Digital Twin – From Science Fiction to Hi-Tech Reality”.65.
Budiardjo
, A.
, and Migliori
, D.
, 2021
, “Digital Twin System Interoperability Framework,” Technical Report, Digital Twin Consortium.66.
Akroyd
, J.
, Mosbach
, S.
, Bhave
, A.
, and Kraft
, M.
, 2020
, “National Digital Twin of the UK – A Knowledge-Graph Approach”.Copyright © 2025 by ASME
You do not currently have access to this content.
