Data processing: artificial intelligence – Neural network – Learning task
Reexamination Certificate
2007-05-29
2007-05-29
Hirl, Joseph P (Department: 2129)
Data processing: artificial intelligence
Neural network
Learning task
C706S006000, C706S012000, C706S014000, C706S015000, C706S032000
Reexamination Certificate
active
10657210
ABSTRACT:
A device for calculating numerical solutions for partial differential equations in successive intervals using adaptive meshes, comprises: a neural network part for producing predictions of gradients at a following interval based on gradients available from previous intervals, and a mesh adaptation part, associated with the neural network part, configured for adapting a mesh over a domain of a respective partial differential equation using the predictions, such that the mesh adaptively refines itself about emerging regions of complexity as the partial differential equation progresses over the successive intervals. The neural network part succeeds in its predictions since its use herein is equivalent to using time series function fitting techniques.
REFERENCES:
Manevitz, Larry, Yousef, Malik; Finite-Element Mesh Generation Using Self-Organizing Neural Networks; Jul. 1997, Computer-Aided Civil & Infrastructure Engineering, vol. 12 Issue 4, p. 233.
Automatic Finite-Element Mesh Generation Using Artificial Neural Networks-Part I: Prediction of Mesh Density; Sep. 1996; IEEE Transactions on Magnetics: vol. 32, No. 5.
Hassoun, Mohamad H.; Fundamentals of Artificial Neural Networks, 1995 MIT Press.
Lagaris et al., Artificial Neural Networks for Solving Ordinary and Partial Differential Equations, IEEE Transactions On Neural Networks, vol. 9, No. 5, Sep. 1998.
Larry Manevitz, Finite-Element Mesh Generation Using Self-Organizing Neural Networks, Jul. 1997, Computer-Aided Civil & Infrastructure Engineering, Vo.l 32 No. 5, 233-250.
R. Chedid et al, Automatic Finite-Element Mesh generation Using Artificial Neural Networks—Part 1: Prediction of Mesh Density, Sep. 1996, IEEE Transactions on Magnetics, vol. 32, No. 5, 5173-5178.
Larry Manevitz, Finite-Element Mesh Adaption via Time Series Prediction Using Neural Networks, Dec. 2, 2001, The Sixth Online World Conference on Soft Computing in Industrial Applications, 769-782.
Bitar Akram
Givoli Dan
Manevitz Larry
Carmel - Haifa University Economic Corporation Ltd.
Hirl Joseph P
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