2 papers
math.NA2025
A framework of discontinuous Galerkin neural networks for iteratively approximating residuals
Long Yuan, Hongxing Rui
We propose an abstract discontinuous Galerkin neural network (DGNN) framework for analyzing the convergence of least-squares methods based on the residual minimization when feasibl…
math.NA2025
Discontinuous hybrid neural networks for the one-dimensional partial differential equations
Xiaoyu Wang, Long Yuan, Yao Yu
A feedforward neural network, including hidden layers, motivated by nonlinear functions (such as Tanh, ReLU, and Sigmoid functions), exhibits uniform approximation properties in So…