3 papers
math.NA2026
Exact Representation of Piecewise Polynomial Finite Element Functions by Two-Hidden-Layer Multilayer Perceptrons
Jun Hu, Pengzhan Jin, Shengyang Xu
We construct exact representations of finite element functions of arbitrary polynomial degree on simplicial meshes in any spatial dimension by two-hidden-layer multilayer perceptro…
math.NA2025
Manifold Function Encoder: Identifying Different Functions Defined on Different Manifolds
Jun Hu, Pengzhan Jin, Weijun Zhang
We propose the Manifold Function Encoder (MFE) for identifying different functions defined on different manifolds. Both a manifold in Euclidean space and a function defined on this…
math.NA2024
A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples
Jun Hu, Pengzhan Jin
We propose a hybrid iterative method based on MIONet for PDEs, which combines the traditional numerical iterative solver and the recent powerful machine learning method of neural o…