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- W2935339072 abstract "We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy. In this procedure, a coarse grid of training points is used at the initial training stages, while more points are added at later stages based on the value of the residual at a larger set of evaluation points. This method increases the robustness of the neural network approximation and can result in significant computational savings, particularly when the solution is non-smooth. Numerical results are presented for benchmark problems for scalar-valued PDEs, namely Poisson and Helmholtz equations, as well as for an inverse acoustics problem." @default.
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- W2935339072 date "2019-01-01" @default.
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- W2935339072 title "Artificial Neural Network Methods for the Solution of Second Order Boundary Value Problems" @default.
- W2935339072 doi "https://doi.org/10.32604/cmc.2019.06641" @default.
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