5 citations · 5 across the 8 of their papers we have counts for
4 papers · 1 filter
Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples
Xinliang Liu, Tong Mao, Jinchao Xu
We develop a rigorous theory of discrete residual least-squares approximation for elliptic spectral equations using linearized ReLU neural networks on the sp…
McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation
Jiwei Jia, Xinliang Liu, Juntao Wang +1
Solving heterogeneous Helmholtz equations at high wavenumbers remains challenging because the discretized operator is indefinite, pollution degrades phase accuracy, and scalar coar…
Condition Numbers and Eigenvalue Spectra of Shallow Networks on Spheres
Xinliang Liu, Tong Mao, Jinchao Xu
We present an estimation of the condition numbers of the \emph{mass} and \emph{stiffness} matrices arising from shallow ReLU neural networks defined on the unit sphere~$\mathbb…
Integral Representations of Sobolev Spaces via ReLU Activation Function and Optimal Error Estimates for Linearized Networks
Xinliang Liu, Tong Mao, Jinchao Xu
This paper presents two main theoretical results concerning shallow neural networks with ReLU activation functions. We establish a novel integral representation for Sobolev spa…