3 papers
math.NA2026
Sparsely connected neural network representation of Lagrange finite element function
Jiaxiong Hao, Yunqing Huang, Nianyu Yi
We construct a mesh-induced sparsely connected neural network framework that exactly reproduces arbitrary-order Lagrange finite element spaces over simplicial meshes. Unlike conven…
math.NA2025
DataTransfer: Neural network based interpolation across non-nested meshes
Jiaxiong Hao, Yunqing Huang, Nianyu Yi
In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great…
math.NA2025
Neural network-enhanced -adaptive finite element algorithm for parabolic equations
Jiaxiong Hao, Yunqing Huang, Nianyu Yi +1
In this paper, we propose a novel -adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional -adaptive fin…