- 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 = "
http://www.soton.ac.uk/~as7/publ/IEEE.pdf",
-
DOI = "
doi:10.1109/TEVC.2007.908467",
-
URL = "
http://results.ref.ac.uk/Submissions/Output/3377591",
- size = "10 pages",
- abstract = "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' problems.",
