Comparing two ways of inferring a differential equation model via Grammar-based Immune Programming

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@InProceedings{Bernardino:2010:CILAMCE,
  author =       "Heder Soares Bernardino and 
                 Helio Jose Correa Barbosa",
  title =        "Comparing two ways of inferring a differential
                 equation model via Grammar-based Immune Programming",
  booktitle =    "Proceedings of the Iberian Latin American Congress on
                 Computational Methods in Engineering (CILAMCE)",
  year =         "2010",
  editor =       "Eduardo Dvorkin and Marcela Goldschmit and 
                 Mario Storti",
  pages =        "9107--9124",
  address =      "Buenos Aires",
  month =        nov # " 15-18",
  organisation = "University of Buernos Aires",
  publisher =    "Asociacion Argentina de Mecanica Computacional
                 http://www.amcaonline.org.ar",
  keywords =     "genetic algorithms, genetic programming, grammatical
                 evolution, Artificial immune systems, grammar-based
                 immune programming, symbolic regression, model
                 inference",
  URL =          "http://www.cimec.org.ar/ojs/index.php/mc/article/view/3656/3569",
  size =         "18 pages",
  abstract =     "An ordinary differential equation (ODE) is a
                 mathematical form to describe physical or biological
                 systems composed by time-derivatives of physical
                 positions or chemical concentrations as a function of
                 its current state. Given observed pairs, a relevant
                 modelling problem is to find the symbolic expression of
                 a differential equation which mathematically describes
                 the concerned phenomenon.

                 The Grammar-based Immune Programming (GIP) is a method
                 for evolving programs in an arbitrary language by
                 immunological inspiration. A program can be a computer
                 program, a numerical function in symbolic form, or a
                 candidate design, such as an analogue circuit. GIP can
                 be used to solve symbolic regression problems in which
                 the objective is to find an analytical expression of a
                 function that better fits a given data set.

                 At least two ways are available to solve model
                 inference problems in the case of ordinary differential
                 equations by means of symbolic regression techniques.
                 The first one consists in taking numerical derivatives
                 from the given data obtaining a set of approximations.
                 Then a symbolic regression technique can be applied to
                 these approximations. Another way is to numerically
                 integrate the ODE corresponding to the candidate
                 solution and compare the results with the observed
                 data.

                 Here, by means of numerical experiments, we compare the
                 relative performance of these two ways to infer models
                 using the GIP method.",
  notes =        "paper ID-1364
                 https://sites.google.com/a/mecom2010.net/mecom-2010/home/Final.pdf?attredirects=0
                 mecom2010.net

                 CILAMCE / ABMEC
                 https://sites.google.com/a/mecom2010.net/mecom-2010/silamce-abmec",
}

Genetic Programming entries for Heder Soares Bernardino Helio J C Barbosa

Citations