4 citations · 10 across the 8 of their papers we have counts for
8 papers
Learn Singularly Perturbed Solutions via Homotopy Dynamics
Chuqi Chen, Yahong Yang, Yang Xiang +1
Solving partial differential equations (PDEs) using neural networks has become a central focus in scientific machine learning. Training neural networks for singularly perturbed pro…
Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers
Chuqi Chen, Qixuan Zhou, Yahong Yang +2
Neural network-based methods have emerged as powerful tools for solving partial differential equations (PDEs) in scientific and engineering applications, particularly when handling…
Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations
Chuqi Chen, Yahong Yang, Yang Xiang +1
Neural network-based approaches have recently shown significant promise in solving partial differential equations (PDEs) in science and engineering, especially in scenarios featuri…
Nearly Optimal Approximation Rates for Deep Super ReLU Networks on Sobolev Spaces
Yahong Yang, Yue Wu, Haizhao Yang +1
This paper introduces deep super ReLU networks (DSRNs) as a method for approximating functions in Sobolev spaces measured by Sobolev norms for with $m\ge…
Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives
Yahong Yang, Haizhao Yang, Yang Xiang
This paper addresses the problem of nearly optimal Vapnik--Chervonenkis dimension (VC-dimension) and pseudo-dimension estimations of the derivative functions of deep neural network…
Stochastic Continuum Models for High--Entropy Alloys with Short-range Order
Yahong Yang, Luchan Zhang, Yang Xiang
High entropy alloys (HEAs) are a class of novel materials that exhibit superb engineering properties. It has been demonstrated by extensive experiments and first principles/atomist…
Approximation of Functionals by Neural Network without Curse of Dimensionality
Yahong Yang, Yang Xiang
In this paper, we establish a neural network to approximate functionals, which are maps from infinite dimensional spaces to finite dimensional spaces. The approximation error of th…
Convergence from Atomistic Model to Peierls-Nabarro Model for Dislocations in Bilayer System with Complex Lattice
Yahong Yang, Tao Luo, Yang Xiang
In this paper, we prove the convergence from the atomistic model to the Peierls--Nabarro (PN) model of two-dimensional bilayer system with complex lattice. We show that the displac…