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2010 Volume 25
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RESEARCH ARTICLE   Open Access    

Learning Qualitative Differential Equation models: a survey of algorithms and applications

  • 1.

    Computational Intelligence Group, College of Computer Science and Technology

  • 2.

    Department of Computing Science

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RESEARCH ARTICLE   Open Access    

Learning Qualitative Differential Equation models: a survey of algorithms and applications

  • 1.

    Computational Intelligence Group, College of Computer Science and Technology

  • 2.

    Department of Computing Science

  • Published online: 01 March 2010
The Knowledge Engineering Review  25,  Article number: 10.1017/S0269888909990348  (2010)  |  Cite this article

Abstract: Abstract: Over the last two decades, qualitative reasoning (QR) has become an important domain in Artificial Intelligence. QDE (Qualitative Differential Equation) model learning (QML), as a branch of QR, has also received an increasing amount of attention; many systems have been proposed to solve various significant problems in this field. QML has been applied to a wide range of fields, including physics, biology and medical science. In this paper, we first identify the scope of this review by distinguishing QML from other QML systems, and then review all the noteworthy QML systems within this scope. The applications of QML in several application domains are also introduced briefly. Finally, the future directions of QML are explored from different perspectives.

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    Acknowledgments

    • We appreciate the support from the National Natural Science Foundation of China under the Grant nos. 60433020, 60673099 and 60773095. WP is financially supported by a joint scholarship of the University of Aberdeen and China Scholarship Council. WP and GMP are supported by the CRISP project (Combinatorial Responses In Stress Pathways) funded by the BBSRC (BB/F00513X/1) under the Systems Approaches to Biological Research (SABR) Initiative.

    • The source code of GOLEM can be downloaded from http://www.doc.ic.ac.uk/~shm/Software/golem/src.tar

    • The experimental data used in GOLEM for learning U-Tube can be accessed from ftp://ftp.cs.york.ac.uk/pub/ML_GROUP/Datasets/utube/golem/utube.tar.Z

    • In QSIM, corresponding values of a constraint are defined as tuples of landmark values that variables in this constraint can take at the same time.

    • In QSI, The defining constraint of a variable, say variable A, is defined as the constraint of which variable A appears on the left-hand side of the corresponding mathematical equation.

    • Exogenous variables are those variables determined from outside the model.

    • The concept of defining constraint is taken from QSI. In QML-Morven, a defining constraint for a variable is the constraint in which this variable or its derivatives appear in the leftmost position.

    • The system variables are all the endogenous variables in a model.

    • In a causally ordered model, the state variables are those variables whose magnitudes only appear on the right-hand side of the qualitative constraints, and whose first derivatives must appear at least once on the left-hand side of some qualitative constraints.

    • All the experiments were performed on a computer cluster with eight compute nodes, each of which has two Opteron 850 (2.4 GHz) CPUs and 4 GB RAM.

    • The result is based on the average value of 10 trials.

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    Cite this article
    Wei Pang, George M. Coghill. 2010. Learning Qualitative Differential Equation models: a survey of algorithms and applications. The Knowledge Engineering Review. 25:348 doi: 10.1017/S0269888909990348
    Wei Pang, George M. Coghill. 2010. Learning Qualitative Differential Equation models: a survey of algorithms and applications. The Knowledge Engineering Review. 25:348 doi: 10.1017/S0269888909990348
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