2 papers
math.NA2025
A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions
Yaqin Zhang, Ke Li, Zhipeng Chang +3
This paper proposes a Kolmogorov high order deep neural network (K-HOrderDNN) for solving high-dimensional partial differential equations (PDEs), which improves the high order deep…
math.NA2024
Adaptive Basis-inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features
Ke Li, Yaqin Zhang, Yunqing Huang +2
This paper proposes an Adaptive Basis-inspired Deep Neural Network (ABI-DNN) for solving partial differential equations with localized phenomena such as sharp gradients and singula…