137 citations · 147 across the 7 of their papers we have counts for
8 papers · 1 filter
A concurrent global-local numerical method for multiscale parabolic equations
Yulei Liao, Yang Liu, Pingbing Ming
This paper presents a concurrent global-local numerical method for solving multiscale parabolic equations in divergence form. The proposed method employs hybrid coefficient to prov…
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…
A broken Hardy inequality on finite element space and application to strain gradient elasticity
Yulei Liao, Pingbing Ming
We illustrate a broken Hardy inequality on discontinuous finite element spaces, blowing up with a logarithmic factor with respect to the meshes size. This is motivated by numerical…
Heterogeneous multiscale methods for fourth-order singular perturbations
Yulei Liao, Pingbing Ming
We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from hete…
Spectral Barron space for deep neural network approximation
Yulei Liao, Pingbing Ming
We prove the sharp embedding between the spectral Barron space and the Besov space with embedding constants independent of the input dimension. Given the spectral Barron space as t…
A pre-training deep learning method for simulating the large bending deformation of bilayer plates
Xiang Li, Yulei Liao, Pingbing Ming
We propose a deep learning based method for simulating the large bending deformation of bilayer plates. Inspired by the greedy algorithm, we propose a pre-training method on a seri…
Taylor-Hood like finite elements for nearly incompressible strain gradient elasticity problems
Yulei Liao, Pingbing Ming, Yun Xu
We propose a family of mixed finite elements that are robust for the nearly incompressible strain gradient model, which is a fourth-order singular perturbed elliptic system. The el…
Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions
Yulei Liao, Pingbing Ming
We propose a new method to deal with the essential boundary conditions encountered in the deep learning-based numerical solvers for partial differential equations. The trial functi…