  The purpose of this study is to utilize the Chebyshev spectral method neural
network(CSNN) model to solve differential equations. This approach employs a
single-layer neural network wherein Chebyshev spectral methods are used to
construct neurons satisfying boundary conditions. The study uses a feedforward
neural network model and error backpropagation principles, utilizing automatic
differentiation (AD) to compute the loss function. This method avoids the need
to solve non-sparse linear systems, making it convenient for algorithm
implementation and solving high-dimensional problems. The unique sampling
method and neuron architecture significantly enhance the training efficiency
and accuracy of the neural network. Furthermore, multiple networks enables the
Chebyshev spectral method to handle equations on more complex domains. The
numerical efficiency and accuracy of the CSNN model are investigated through
testing on elliptic partial differential equations, and it is compared with the
well-known Physics-Informed Neural Network(PINN) method.
