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Solution of ODE/PDE’s using RBF Neural Networks

Solution of ODE/PDE’s using RBF Neural Networks. Tim A. Handy. Example Problem. Approximate the solution of:. Solving Using RBF NN. Solving Using RBF NN. Approximation. Plug y(x) into goal equations Solve system

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Solution of ODE/PDE’s using RBF Neural Networks

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  1. Solution of ODE/PDE’s using RBF Neural Networks Tim A. Handy

  2. Example Problem • Approximate the solution of:

  3. Solving Using RBF NN

  4. Solving Using RBF NN

  5. Approximation

  6. Plug y(x) into goal equations • Solve system • Can apply K-means clustering to modify the centers of the RBFs. Allows “refinement” of RBF locations by sampling more in one area. • Boundary layer refinement in flows • High gradient areas • Not really done in the literature

  7. Proposal Objective: Apply RBF NN’s to solve ODE/PDE’s and utilize clustering algorithms to increase accuracy in specific areas.

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