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:对物理系统的完全理解需要精确和符合自然保护法的模型。最近的代表学习趋势包括从数据中学习拉格朗格语,而不是直接发现运动的正方程式。等式发现技术的普及具有巨大的潜力;然而,现有的拉格朗加语的发现框架是黑箱性质。这引起了人们对所发现拉格朗加语的可重复性的关切。在本条中,我们建议采用新的数据驱动机器学习算法,将可解释的拉格朗加语从数据中自动发现出来。拉格朗格语以可解释的形式产生,这也使得能够自动发现保护法和调节运动方程式。拟议框架的结构的设计能够使拉格朗格语从一个基本领域的一个分支中学习,然后推广一个无限的系统。拟议框架的忠实性以普通差异方程式和部分差异方程式所描述的示例为示例,这些系统可以知道拉格朗加语和受保护的方程式的数量。