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Spectral Convergence of Random Feature Method in Multiple Dimensions
Pingbing Ming, Hao Yu
We first prove spectral convergence of the random feature method (RFM) for multidimensional targets in Sobolev, Gevrey, ultra-analytic, and bandlimited classes. The analysis establ…
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…
Spectral convergence of random feature method in one dimension
Pingbing Ming, Hao Yu
We first prove the spectral convergence of the random feature method (RFM) when used to solve second-order elliptic equations and eigenvalue problems in one dimension, provided tha…
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. The…