155 citations · 987 across the 104 of their papers we have counts for
11 papers · 1 filter
Uniform Inf-Sup Norm Equivalence and Robust Operator Preconditioning for Stokes Flow in tight domains with Periodic Pillars
Qi Xin, Yan Xie, Chen-song Zhang +2
Many microfluidic and porous-media computations reduce to the same core task: solving a Stokes saddle-point system on a domain perforated by a dense periodic array of pillars, as i…
Sharp Sobolev Approximation on General Domains by Linearized Shallow Networks with Analytic Activations
Jia Li, Tong Mao, Jinchao Xu
We study Sobolev approximation on bounded domains by linearized shallow neural networks whose inner parameters are prescribed independently of the target function. Our main step is…
Sharp Approximation on the Sphere by Linearized Shallow Networks with Analytic Activations
Jia Li, Tong Mao, Jinchao Xu
We study the spectral behavior and approximation properties of linearized shallow networks with analytic activation functions on the unit sphere . Motivated by earlier…
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…
Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View
Tong Mao, Jinchao Xu
Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom. However, practical computation operates under finite precisi…
ReLU Neural de Rham Complexes
Kaibo Hu, Jindong Wang, Jinchao Xu
We construct finite-dimensional de Rham subcomplexes generated by fixed-neuron shallow ReLU neural networks, a class of spaces known to provide optimal approximation rates. For…
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…
Sharp inf-sup estimate for the Stokes equation in tight domains with periodic pillars and some numerical implications
Qi Xin, Shihua Gong, Jinchao Xu
The predictive simulation of fluid dynamics in densely packed microfluidic devices, such as Deterministic Lateral Displacement (DLD) arrays, stagnates with standard iterative solve…
High-order DLM-ALE discretizations with robust operator preconditioning for fluid-rigid-body interaction
Qi Xin, Shihua Gong, Lingyue Shen +5
Motivated by the design of deterministic lateral displacement (DLD) microfluidic devices, we develop a high-order numerical framework for fluid-rigid-body interaction on fitted mov…
A quasi-monolithic localized high-order ALE finite element method for multi-scale fluid-structure interaction problems
Lingyue Shen, Qi Xin, Yan Chen +4
This paper presents a quasi-monolithic localized high-order arbitrary Lagrangian-Eulerian (qMLH-ALE) finite element method for multi-scale fluid-structure interaction (FSI) in micr…
Solving High-Dimensional PDEs Using Linearized Neural Networks
Tong Mao, Jinchao Xu, Xiaofeng Xu
Linearized shallow neural networks that are constructed by fixing the hidden-layer parameters have recently shown strong performance in solving partial differential equations (PDEs…