CLPNets:用于具有对称性的多部分哈密尔顿系统的合李-波松神经网络
Christopher Eldred1, François Gay-Balmaz2, Vakhtang Putkaradze3
1Computer Science Research Institute, Sandia National Laboratory, 1450 Innovation Pkwy SE, Albuquerque, NM, 87123, USA.
概括
我们介绍了相结合的Lie-Poisson神经网络 (CLPNets),用于精确的基于数据的预测复杂的哈密尔顿系统. 这种新的方法保留了基本结构,并处理相互作用的组件,优于现有的技术.
科学领域:
- 计算物理学的计算物理.
- 几何力学是几何力学的一个方面.
- 机器学习是机器学习.
背景情况:
- 准确预测哈密尔顿系统需要结构保存方法.
- 与李群元素 (例如,SE(3) 相互作用的系统对现有的基于数据的计算构成挑战.
- 弹性棒的分离是这样一个复杂系统的例子.
研究的目的:
- 为复杂的哈密尔顿系统开发一种新的基于数据的计算和相位空间学习方法.
- 保持这些系统固有的Lie-Poisson结构.
- 在相对位置和方向上解决李群值元素所带来的挑战.
主要方法:
- 介绍基于SympNets和LPNets的合谎言-普森神经网络 (CLPNets).
- 用相位空间映射设计神经网络,以保持李-波松结构.
- 将CLPNets应用于逐渐复杂的系统:双体旋转,自由刚性体旋转和相互作用的SE(3) 组件.
主要成果:
- CLPNets 保存卡西米尔不变数以达到机器精度和高精度的能量.
- 该方法证明了对维度的诅咒的抵抗力,对于高维系统 (3-18D) 需要最小的数据点 (数千).
- 对于复杂的案例,CLPNets表现出大约200个参数的记忆效率.
结论:
- CLPNets提供了一个强大而高效的解决方案,用于基于数据的预测,复杂的哈密尔顿式系统与相互作用的组件.
- 该方法成功处理涉及李群元素的系统,对于连续力学等应用至关重要.
- 在将机器学习应用于几何力学方面,CLPNets代表了重大进展.
相关概念视频
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