TY - JOUR
T1 - Neural Network Method for Integral Fractional Laplace Equations
AU - Hao , Zhaopeng
AU - Park , Moongyu
AU - Cai , Zhiqiang
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 95
EP - 118
PY - 2023
DA - 2023/01
SN - 13
DO - http://doi.org/10.4208/eajam.010122.210722
UR - https://global-sci.org/intro/article_detail/eajam/21304.html
KW - Deep Ritz method, neural network, fractional elliptic PDE, ReLU.
AB - <p style="text-align: justify;">A neural network method for fractional order diffusion equations with integral fractional Laplacian is studied. We employ the Ritz formulation for the corresponding fractional equation and then derive an approximate solution of an optimization problem in the function class of neural network sets. Connecting the neural network sets with
weighted Sobolev spaces, we prove the convergence and establish error estimates of the
neural network method in the energy norm. To verify the theoretical results, we carry
out numerical experiments and report their outcome.</p>