Learning solutions to partial differential equations using LS-SVM

Siamak Mehrkanoon*, Johan A.K. Suykens

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


This paper proposes an approach based on Least Squares Support Vector Machines (LS-SVMs) for solving second order partial differential equations (PDEs) with variable coefficients. Contrary to most existing techniques, the proposed method provides a closed form approximate solution. The optimal representation of the solution is obtained in the primal-dual setting. The model is built by incorporating the initial/boundary conditions as constraints of an optimization problem. The developed method is well suited for problems involving singular, variable and constant coefficients as well as problems with irregular geometrical domains. Numerical results for linear and nonlinear PDEs demonstrate the efficiency of the proposed method over existing methods.

Original languageEnglish
Pages (from-to)105-116
Number of pages12
Issue number1
Publication statusPublished - 2015


  • Closed form approximate solution
  • Collocation method
  • Least squares support vector machines
  • Partial differential equations


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