.png){kind=icon}
返回
SelectNet: Self-paced learning for high-dimensional partial differential equations
.png){kind=icon}
OA
AI
DOI：10.1016/j.jcp.2021.110444.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
The least squares method with deep neural networks as function parametrization has been applied to solve certain high-dimensional partial differential equations (PDEs) successfully; however, its convergence is slow and might not be guaranteed even within a simple class of PDEs. To improve the convergence of the network-based least squares model, we introduce a novel self-paced learning framework, SelectNet, which quantifies the difficulty of training samples, treats samples equally in the early stage of training, and slowly explores more challenging samples, e.g., samples with larger residual errors, mimicking the human cognitive process for more efficient learning. In particular, a selection network and the PDE solution network are trained simultaneously; the selection network adaptively weighting the training samples of the solution network achieving the goal of self-paced learning. Numerical examples indicate that the proposed SelectNet model outperforms existing models on the convergence speed and the convergence robustness, especially for low-regularity solutions. (c) 2021 Elsevier Inc. All rights reserved.
Keyword:
High-dimensional PDEs
Deep neural networks
Self-paced learning
Selected sampling
Least square method
Convergence
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
3.8
论文数:
1.6W
被引数:
7.4W
机构
引用论文
.png){kind=icon}
Real-time and offline techniques for identifying obstructive sleep apnea patients用于识别阻塞性睡眠呼吸暂停患者的实时和离线技术
PREAI
分享收藏Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations物理信息神经网络: 一种用于解决涉及非线性偏微分方程的正反问题的深度学习框架OAAI
OAAI分享收藏Order of maturation of the components of the working memory from childhood to emerging adulthood从童年到成年的工作记忆成分的成熟顺序OAAI
OAAI分享收藏
查看更多内容