齐次空间
人工神经网络
哈密顿量(控制论)
能量守恒
守恒定律
广义相对论
拉格朗日
消散
正则坐标
多样性(控制论)
物理
计算机科学
经典力学
理论物理学
数学
人工智能
数学优化
量子力学
几何学
相空间
作者
Miles Cranmer,Sam Greydanus,Stephan Hoyer,Peter W. Battaglia,David N. Spergel,Shirley Ho
出处
期刊:Cornell University - arXiv
日期:2020-01-01
被引量:77
标识
DOI:10.48550/arxiv.2003.04630
摘要
Accurate models of the world are built upon notions of its underlying symmetries. In physics, these symmetries correspond to conservation laws, such as for energy and momentum. Yet even though neural network models see increasing use in the physical sciences, they struggle to learn these symmetries. In this paper, we propose Lagrangian Neural Networks (LNNs), which can parameterize arbitrary Lagrangians using neural networks. In contrast to models that learn Hamiltonians, LNNs do not require canonical coordinates, and thus perform well in situations where canonical momenta are unknown or difficult to compute. Unlike previous approaches, our method does not restrict the functional form of learned energies and will produce energy-conserving models for a variety of tasks. We test our approach on a double pendulum and a relativistic particle, demonstrating energy conservation where a baseline approach incurs dissipation and modeling relativity without canonical coordinates where a Hamiltonian approach fails. Finally, we show how this model can be applied to graphs and continuous systems using a Lagrangian Graph Network, and demonstrate it on the 1D wave equation.
科研通智能强力驱动
Strongly Powered by AbleSci AI