“…With the development of computer technology and the improvement of neural network theory, the neural network has been applied to various fields, such as approximating (Park and Sandberg, 1991;Hou et al, 2009;Hou and Han, 2010, forecasting , image classification (Yan et al, 2014), information processing (Kötter and Stephan, 2003), face recognition (Kim et al, 2017), finite deformation hyperelasticity and solving Des . At present, there are many neural networks for solving DEs, such as wavelet neural network (Li, 2010), cellular neural networks (Aein and Talebi, 2009;Klinkenbusch et al, 2011), finite element neural network (Beltzer et al, 2003), Chebyshev neural network (ChNN) , Legendre neural network (Yang et al, 2018), radial basis function neural network (Rizaner and Rizaner, 2018), Bernstein neural network (BeNN) (Sun et al, 2018) and hybrid neural network (Malek and Beidokhti, 2006). Cosmin et al (2019) proposes a partial differential equation (PDE) solution algorithm based on neural network, which adopts the adaptive configuration strategy, especially for non-smooth solutions, which saves a lot of computation and also improves the robustness of neural network approximation.…”