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.

本文提出了一种使用神经网络来参数化任意 Lagrangian 的 Lagrangian 神经网络（LNNs），该方法不需要标准坐标，因此可适用于标准动量未知或难以计算的情况，并且在各种任务中产生遵守能量守恒条件的模型，通过在双摆和相对论粒子上的测试表明，该方法可用于建模且不会损耗能量，还可以应用于图形和连续系统，并证明其用于一维波动方程。