Sobester, A., Nair, P.B. and Keane, A.J.
Genetic programming approaches for solving elliptic partial differential equations
IEEE Transactions on Evolutionary Computation, 12, (4), . (doi:10.1109/TEVC.2007.908467).
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In 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 optimized 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.
|Digital Object Identifier (DOI):
||boosting, genetic programming (GP), meshfree collocation, partial differential equations (PDEs), radial basis functions
|25 August 2003||Submitted|
|22 February 2008||e-pub ahead of print|
||24 Dec 2008
||16 Apr 2017 17:20
|Further Information:||Google Scholar|
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