3 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.AP2024
Stability for inverse random source problems of the polyharmonic wave equation
Peijun Li, Zhenqian Li, Ying Liang
This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation, where the source is represented by white noise. The study exam…
math.AP2024
Stability estimates of inverse random source problems for the wave equations by using correlation-based data
Peijun Li, Ying Liang, Xu Wang
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a mi…