Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of Hamiltonian and Lagrangian of physical systems. While the existing methods parameterize the Lagrangian using neural networks, we propose an alternate framework for learning interpretable Lagrangian descriptions of physical systems from limited data using the sparse Bayesian approach. Unlike existing neural network-based approaches, the proposed approach (a) yields an interpretable description of Lagrangian, (b) exploits Bayesian learning to quantify the epistemic uncertainty due to limited data, (c) automates the distillation of Hamiltonian from the learned Lagrangian using Legendre transformation, and (d) provides ordinary (ODE) and partial differential equation (PDE) based descriptions of the observed systems. Six different examples involving both discrete and continuous system illustrates the efficacy of the proposed approach.

翻译：学习并预测物理系统动力学需要深刻理解其背后的物理定律。近期有关物理定律学习的研究工作，将方程发现框架推广至物理系统的哈密顿量和拉格朗日量的发现。现有方法通常使用神经网络参数化拉格朗日量，而我们则提出了一种替代框架，利用稀疏贝叶斯方法从有限数据中学习物理系统的可解释拉格朗日描述。与现有基于神经网络的方法不同，所提方法能够：(a) 提供拉格朗日量的可解释描述；(b) 利用贝叶斯学习量化因数据有限导致的认知不确定性；(c) 通过勒让德变换自动从所学拉格朗日量中蒸馏出哈密顿量；(d) 提供基于常微分方程和偏微分方程的观测系统描述。六个涉及离散与连续系统的不同示例验证了所提方法的有效性。