.png){kind=icon}
返回
The deep minimizing movement scheme
.png){kind=icon}
OA
AI
DOI：10.1016/j.jcp.2023.112518.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
Solutions of certain partial differential equations (PDEs) are often represented by the steepest descent curves of corresponding functionals. Minimizing movement scheme was developed in order to study such curves in metric spaces. Especially, Jordan-Kinderlehrer-Otto studied the Fokker-Planck equation in this way with respect to the Wasserstein metric space. In this paper, we propose a deep learning-based minimizing movement scheme for approximating the solutions of PDEs. The proposed method is highly scalable for high-dimensional problems as it is free of mesh generation. We demonstrate through various kinds of numerical examples that the proposed method accurately approximates the solutions of PDEs by finding the steepest descent direction of a functional even in high dimensions.
Keyword:
Minimizing movement scheme
JKO scheme
Neural networks
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
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
.png){kind=icon}
PREAI
分享收藏Improving the accuracy and consistency of the scalar auxiliary variable (SAV) method with relaxationOAAI
OAAI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Trend to equilibrium for the kinetic Fokker-Planck equation via the neural network approach通过神经网络方法实现动力学fokker-planck方程的平衡趋势OAAI
OAAI分享收藏
查看更多内容