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