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使用WSINDy的粗粒型哈密尔顿系统.

Daniel A Messenger1, Joshua W Burby2, David M Bortz3

  • 1Department of Applied Mathematics, University of Colorado, Boulder, CO, 80309-0526, USA. daniel.messenger@colorado.edu.

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|June 24, 2024
PubMed
概括
此摘要是机器生成的。

弱形式方程学习,一种称为WSINDy的方法,有效地识别了减少的哈密尔顿系统. 这种方法对噪声和干扰具有强度,因此非常适合粗粒度复杂动态.

关键词:
粗粒的 粗粒的 粗粒的哈密尔顿式系统是哈密尔顿式系统.华盛顿 - 辛迪

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科学领域:

  • 计算物理 计算物理
  • 动态系统 动态系统
  • 应用数学 应用数学 应用数学

背景情况:

  • 弱形式方程学习和替代模型是计算效率高且强大的,用于发现由ODEs,PDEs和SDEs控制的动态.
  • 像同质化和平均场描述这样的粗粒度技术用于相互作用的粒子系统.
  • 具有近似对称性的哈密尔顿动态,通常与时间尺度分离相关,在导出减少顺序模型方面存在挑战.

研究的目的:

  • 为了扩展弱形式方程的学习,以粗粒度的哈密尔顿动力学与近似对称.
  • 为了证明WSINDy (非线性动力学的弱形式稀疏识别) 在识别减少的哈密尔顿系统方面的能力.
  • 为该方法在哈密尔顿粗粒化中的有效性提供理论证明.

主要方法:

  • 利用WSINDy从数据中识别减少的哈密尔顿系,利用其通过限制哈密尔顿向量场的基础来保护哈密尔顿结构的能力.
  • 采用单一的轨迹来学习全球缩小的哈密尔顿式,避免了计算上昂贵的前置解决方案.
  • 将方法应用于近周期的哈密尔顿系,表现出近似对称性.

主要成果:

  • WSINDy成功地确定了减少的哈密尔顿系统,即使有大量的扰动和外部噪声.
  • 该方法实现了至少两次的尺寸缩小,准确地捕捉了领先顺序的动态.
  • 一个理论贡献证明了第一阶平均化在近周期的哈密尔顿系统中保留了哈密尔顿结构,这证明了WSINDy方法的合理性.

结论:

  • 弱形式方程学习,特别是WSINDy,是用于哈密尔顿粗粒度的计算效率高和强大的方法.
  • 该方法有效地识别了近似对称的系统的减少顺序模型,保留了底层的哈密尔顿结构.
  • 该方法的有效性通过物理相关的例子来说明,包括合振荡器和带电粒子动力学.