Realistic models of physical world rely on differentiable symmetries that, in turn, correspond to conservation laws. Recent works on Lagrangian and Hamiltonian neural networks show that the underlying symmetries of a system can be easily learned by a neural network when provided with an appropriate inductive bias. However, these models still suffer from issues such as inability to generalize to arbitrary system sizes, poor interpretability, and most importantly, inability to learn translational and rotational symmetries, which lead to the conservation laws of linear and angular momentum, respectively. Here, we present a momentum conserving Lagrangian neural network (MCLNN) that learns the Lagrangian of a system, while also preserving the translational and rotational symmetries. We test our approach on linear and non-linear spring systems, and a gravitational system, demonstrating the energy and momentum conservation. We also show that the model developed can generalize to systems of any arbitrary size. Finally, we discuss the interpretability of the MCLNN, which directly provides physical insights into the interactions of multi-particle systems.
翻译:物理世界的现实模型依赖于不同的可互换的对称性,而这些对称性反过来又与养护法相对应。关于拉格朗吉亚和汉密尔顿神经网络的近期工作表明,当一个神经网络获得适当的感应性偏差时,一个系统的基本对称性很容易被神经网络所了解。然而,这些模型仍然受到一些问题的困扰,例如无法概括到任意的系统大小,解释性差,而且最重要的是,无法学习翻译和轮换的对称性,这分别导致线性和角性动力的养护法。在这里,我们展示了保护拉格朗吉亚神经网络的势头(MMCLNN),它学习了系统的拉格朗吉亚人,同时也保存了翻译和旋转的对称性。我们在线性和非线性弹簧系统和引力系统上测试了我们的方法,显示了能量和动力的保持。我们还表明,所开发的模型可以概括到任何任意性的系统。最后,我们讨论了MCLNN的可解释性,它直接为多粒系统的互动提供物理洞察力。