Genetic Programming Approaches for Solving Elliptic Partial Differential Equations

Created by W.Langdon from gp-bibliography.bib Revision:1.4340

  author =       "Andras Sobester and Prasanth B. Nair and 
                 Andy J. Keane",
  title =        "Genetic Programming Approaches for Solving Elliptic
                 Partial Differential Equations",
  journal =      "IEEE Transactions on Evolutionary Computation",
  year =         "2008",
  volume =       "12",
  number =       "4",
  pages =        "469--478",
  month =        aug,
  keywords =     "genetic algorithms, genetic programming, elliptic
                 equations, genetic algorithms, least squares
                 approximations, mathematics computing, partial
                 differential equations, radial basis function networks,
                 boundary conditions, elliptic partial differential
                 equations, genetic programming, geometrically irregular
                 domains, gradient boosting, least-squares collocation
                 principle, machine learning community, radial basis
                 function network Boosting, genetic programming (GP),
                 meshfree collocation, partial differential equations
                 (PDEs), radial basis functions",
  ISSN =         "1089-778X",
  URL =          "",
  DOI =          "doi:10.1109/TEVC.2007.908467",
  URL =          "",
  abstract =     "n this paper, we propose a technique based on genetic
                 programming (GP) for meshfree solution of elliptic
                 partial differential equations. We employ the
                 least-squares collocation principle to define an
                 appropriate objective function, which is optimised
                 using GP. Two approaches are presented for the repair
                 of the symbolic expression for the field variables
                 evolved by the GP algorithm to ensure that the
                 governing equations as well as the boundary conditions
                 are satisfied. In the case of problems defined on
                 geometrically simple domains, we augment the solution
                 evolved by GP with additional terms, such that the
                 boundary conditions are satisfied by construction. To
                 satisfy the boundary conditions for geometrically
                 irregular domains, we combine the GP model with a
                 radial basis function network. We improve the
                 computational efficiency and accuracy of both
                 techniques with gradient boosting, a technique
                 originally developed by the machine learning community.
                 Numerical studies are presented for operator problems
                 on regular and irregular boundaries to illustrate the
                 performance of the proposed algorithms.",
  notes =        "Also known as \cite{4455556}",
  uk_research_excellence_2014 = "Significance of output:

                 This is a step towards an 'automated discovery engine'.
                 The automated analytical solution of partial
                 differential equations (which this paper proposes a
                 method for) is a 'blue sky' area at the moment, but has
                 the potential to yield unexpected physical insights
                 when applied to poorly understood 'real life'

Genetic Programming entries for Andras Sobester Prasanth B Nair Andy J Keane