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PMNO: 一个新的物理引导的多步骤神经运算子预测器,用于部分微分方程.
Jin Song1, Kenji Kawaguchi2, Zhenya Yan3
1School of Advanced Interdisciplinary Science, University of Chinese Academy of Sciences, Beijing, 100190, China; State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China.
由物理指导的多步神经运算器 (PMNO) 改善了长时间的物理系统预测. 这种新的架构通过使用历史数据和隐含的时间步骤来提高外推和培训效率.
科学领域:
- 科学计算是科学计算.
- 机器学习 机器学习
- 基于物理学的神经网络.
背景情况:
- 神经运算符在无限维函数空间之间进行近似映射,用于物理系统模拟.
- 目前的局限性包括有限的表示能力,数据依赖性和差异推断.
- 挑战在复杂的物理系统的长期预测任务中占据着突出地位.
研究的目的:
- 介绍一种新的以物理为导向的多步神经运算器 (PMNO) 架构.
- 解决现有的神经操作员在训练效率和推断性能方面的局限性.
- 提高长视野复杂物理系统的预测准确度.
主要方法:
- 开发了一个PMNO架构,在前向传递中包含多步历史数据.
- 在反向传播过程中使用逆向分化公式 (BDF) 实现了隐式的时间分步方案.
- 采用因果培训策略,以实现高效的端到端优化和分辨率不变外推.
主要成果:
- PMNO显示出增强的抽象能力和更高效,稳定的培训,减少了数据要求.
- 在各种物理系统中实现了卓越的预测性能:2D线性系统,不规则域建模,复杂值波动力学和反应扩散过程.
- 解析度不变属性允许对任意空间分辨率进行快速推断.
结论:
- 在复杂的物理系统中,PMNO框架为长期预测提供了一个强大的解决方案.
- PMNO提高了外推能力和培训效率,需要更少的数据.
- 该架构具有多功能性,允许与各种神经操作员模型 (如FNO和DeepONet) 进行集成.
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