PDE-GANet:部分微分方程的发现由对抗式学习提供动力
Bin Wang1, Yuxuan Gao1, Shenglin Guo1
1School of Electronic Engineering, Xidian University, No. 2, South Taibai Road, Xi'an, Shaanxi, 710071, PR China.
概括
本研究介绍了PDE-GANet,这是一个新的深度学习网络,用于从数据中发现支配部分微分方程 (PDEs). 与现有的方法相比,PDE-GANet在PDE表达和数值溶液估计方面都取得了更高的准确性.
科学领域:
- 计算数学 计算数学 计算数学
- 人工智能的人工智能
- 科学计算科学计算
背景情况:
- 部分微分方程 (PDEs) 对于描述复杂系统至关重要,但很难制定.
- 数据驱动的PDE发现是一个不断增长的研究领域,由深度学习的进步推动.
- 现有的方法在准确地表示和从数据中学习PDE的规则方面存在局限性.
研究的目的:
- 提出一个新的深度学习框架,PDE-GANet,用于从数据中准确有效地发现管理PDEs.
- 通过使用双向网络架构,增强PDE的代表性和学习策略.
- 为了提高PDE表达和数值解决方案估计的准确性.
主要方法:
- 开发了PDE-GANet,这是一个生成对抗网络 (GAN),包含符号网络和循环神经网络.
- 该生成器 (符号网络) 代表PDE表达式并估计数值解决方案.
- 区分器 (循环神经网络) 从时间角度对推断PDE的解决方案进行验证.
主要成果:
- 在从数据中发现PDEs方面,PDE-GANet表现出卓越的性能.
- 与最先进的方法相比,在PDE表达方面取得了更高的准确性.
- 为发现的PDEs提供了更精确的数值解决方案.
结论:
- PDE-GANet为数据驱动的PDE发现提供了一种强大的方法.
- 拟议的方法促进了对复杂系统的PDE的准确制定和解决.
- 这项工作有可能扩大PDE在各种科学和工程学科的应用范围.
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