Cosmin Anitescu1, Elena Atroshchenko2, Naif Alajlan3, Timon Rabczuk3,*
CMC-Computers, Materials & Continua, Vol.59, No.1, pp. 345-359, 2019, DOI:10.32604/cmc.2019.06641
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… More >
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