2 papers
math.NA2026
From Frequency Bias to Spectral Balance: Operator-Aware Preconditioners for PINNs
Roy Y. He, Ying Liang, Hongkai Zhao +1
When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning…
math.NA2025
What Can One Expect When Solving PDEs Using Shallow Neural Networks?
Roy Y. He, Ying Liang, Hongkai Zhao +1
We use elliptic partial differential equations (PDEs) as examples to show various properties and behaviors when shallow neural networks (SNNs) are used to represent the solutions.…