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math.NA2024
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…
math.NA2023★ 3 cited
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…
math.NA2022★ 1 cited
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…