155 citations · 987 across the 104 of their papers we have counts for
4 papers · 1 filter
A neuron-wise subspace correction method for the finite neuron method
Jongho Park, Jinchao Xu, Xiaofeng Xu
In this paper, we propose a novel algorithm called Neuron-wise Parallel Subspace Correction Method (NPSC) for the finite neuron method that approximates numerical solutions of part…
On the Activation Function Dependence of the Spectral Bias of Neural Networks
Qingguo Hong, Jonathan W. Siegel, Qinyang Tan +1
Neural networks are universal function approximators which are known to generalize well despite being dramatically overparameterized. We study this phenomenon from the point of vie…
A sharp Korn's inequality for piecewise space and its application
Qingguo Hong, YounJu Lee, Jinchao Xu
In this paper, we revisit Korn's inequality for the piecewise space based on general polygonal or polyhedral decompositions of the domain. Our Korn's inequality is expressed…
An efficient iterative method for dynamical Ginzburg-Landau equations
Qingguo Hong, Limin Ma, Jinchao Xu
In this paper, we propose a new finite element approach to simulate the time-dependent Ginzburg-Landau equations under the temporal gauge, and design an efficient preconditioner fo…