通用哈密尔顿神经网络用于动态建模:自动处理复杂的约束,并实现坐标自由
IEEE transactions on neural networks and learning systems
|September 4, 2024
概括
本研究介绍了数据驱动建模的一般哈密尔顿神经网络 (GHNN) 框架. GHNN克服了法定坐标的局限性,使和起重机等复杂系统的准确预测成为可能.
科学领域:
- 物理学和工程 物理学和工程
- 机器学习 机器学习
- 动态系统 动态系统
背景情况:
- 集成哈密尔顿形式主义的神经网络 (NN) 改进了数据驱动模型.
- 现有的方法需要未知的法定坐标,限制现实世界的应用.
- 当前的坐标转换或复杂的NN方法缺乏普遍性,并且很难训练.
研究的目的:
- 为哈密尔顿神经网络提出一个多功能,无坐标的框架.
- 为了实现复杂系统的准确建模,而无需事先了解正规坐标.
- 开发一个一般的哈密尔顿神经网络 (GHNN),可以自动处理约束.
主要方法:
- 一般的哈密尔顿NN (GHNN) 框架使用两个神经网络:HNet用于哈密尔顿预测和JNet用于互连矩阵预测.
- 自动分化计算了哈密尔顿数量的梯度.
- 状态差异是通过将梯度与相互连接矩阵乘以得到的,其次是用于状态预测的ODEs的数值集成.
主要成果:
- 在GHNN框架展示了无坐标建模能力.
- 它成功地处理动态系统中的复杂约束.
- 对于非线性简单和双,合和3D起重机系统,可以实现准确的预测.
结论:
- GHNN为嵌入哈密尔顿力学在神经网络中提供了一种通用而简洁的方法.
- 该框架克服了对正规坐标的需求,提高了对现实世界问题的适用性.
- 在多样化和具有挑战性的动态系统中,GHNN显示出显著的准确性和多功能性.
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