TY - JOUR
T1 - A Chebyshev Polynomial Neural Network Solver for Boundary Value Problems of Elliptic Equations
AU - Meng , Liujun
AU - Zhang , Xuelin
AU - Wang , Hanquan
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 230
EP - 245
PY - 2023
DA - 2023/04
SN - 13
DO - http://doi.org/10.4208/eajam.2022-064.210722 
UR - https://global-sci.org/intro/article_detail/eajam/21646.html
KW - Chebyshev polynomial, neural network, elliptic equation, deep learning.
AB - <p style="text-align: justify;">A Chebyshev polynomial neural network for solving boundary value problems
for one- and two-dimensional partial differential equations is constructed. In particular,
the input parameters are expanded by Chebyshev polynomials and fed into the network.
A loss function is constructed, and approximate solutions are determined by minimizing
the loss function. Elliptic equations are used to test a Chebyshev polynomial neural
network solver. The numerical examples illustrate the high accuracy of the method.</p>