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Learning solutions to partial differential equations using LS-SVM
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DOI：10.1016/j.neucom.2015.02.013.png)
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摘要
En 中文
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. (C) 2015 Elsevier B.V. All rights reserved.
Keyword:
Least squares support vector machines
Partial differential equations
Closed form approximate solution
Collocation method
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期刊
IF:
6.5
论文数:
2.5W
被引数:
6.5W
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OAAI分享收藏Comparison of generalization ability on solving differential equations using backpropagation and reformulated radial basis function networks.png)
NEUROCOMPUTING
NEUROCOMPUTINGIF6.5
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