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math.NA2025
Spectral connvergece of random feature method in one dimension
Pingbing Ming, Hao Yu
Among the various machine learning methods solving partial differential equations, the Random Feature Method (RFM) stands out due to its accuracy and efficiency. In this paper, we…
math.NA2025
Sharp uniform approximation for spectral Barron functions by deep neural networks
Yulei Liao, Pingbing Ming, Hao Yu
This work explores the neural network approximation capabilities for functions within the spectral Barron space , where is the smoothness index. We demonstrate t…
math.NA2024
Generalization Error Estimates of Machine Learning Methods for Solving High Dimensional Schrödinger Eigenvalue Problems
Hao Yu, Yixiao Guo, Pingbing Ming
We propose a machine learning method for computing eigenvalues and eigenfunctions of the Schrödinger operator on a -dimensional hypercube with Dirichlet boundary conditions. Th…