A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing equations of motion. The generalization of equation discovery techniques has huge potential; however, existing Lagrangian discovery frameworks are black-box in nature. This raises a concern about the reusability of the discovered Lagrangian. In this article, we propose a novel data-driven machine-learning algorithm to automate the discovery of interpretable Lagrangian from data. The Lagrangian are derived in interpretable forms, which also allows the automated discovery of conservation laws and governing equations of motion. The architecture of the proposed framework is designed in such a way that it allows learning the Lagrangian from a subset of the underlying domain and then generalizing for an infinite-dimensional system. The fidelity of the proposed framework is exemplified using examples described by systems of ordinary differential equations and partial differential equations where the Lagrangian and conserved quantities are known.

翻译：对物理系统的完整理解需要既准确又符合自然守恒定律的模型。表示学习的最新趋势侧重于从数据中学习拉格朗日量，而非直接发现运动控制方程。方程发现技术的泛化具有巨大潜力，然而现有的拉格朗日量发现框架本质上属于黑箱模型，这引发了对所发现拉格朗日量可复用性的担忧。本文提出一种新颖的数据驱动机器学习算法，用于自动从数据中发现可解释的拉格朗日量。这些拉格朗日量以可解释形式推导得出，同时还能自动发现守恒定律和运动控制方程。该框架的架构设计使其能够从底层域的子集学习拉格朗日量，进而推广到无限维系统。通过已知拉格朗日量和守恒量的常微分方程组及偏微分方程组描述的实例，验证了所提框架的可靠性。