TY - EJOU
AU - Anitescu, Cosmin
AU - Atroshchenko, Elena
AU - Alajlan, Naif
AU - Rabczuk, Timon
TI - Artificial Neural Network Methods for the Solution of Second Order Boundary Value Problems
T2 - Computers, Materials \& Continua
PY - 2019
VL - 59
IS - 1
SN - 1546-2226
AB - 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.
KW - Deep learning
KW - adaptive collocation
KW - inverse problems
KW - artificial neural networks
DO - 10.32604/cmc.2019.06641