论文标题
从高度嘈杂和稀疏的数据中发现具有物理信息信息标准的部分微分方程
Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion
论文作者
论文摘要
PDE的数据驱动的发现最近取得了巨大进展，许多规范的PDE已成功地发现了概念验证。但是，在没有事先参考的情况下确定最合适的PDE在实际应用方面仍然具有挑战性。在这项工作中，提出了一个信息信息标准（PIC），以合成发现的PDE的简约和精度。拟议的PIC可以在不同的物理场景中七个规范的PDE上获得最新的鲁棒性，并在七个规范的PDE上获得了最糟糕的数据，这证实了其处理困难情况的能力。该图片还用于从实际物理场景中的微观仿真数据中发现未开采的宏观管理方程。结果表明，发现的宏观PDE精确且简约，并满足基础的对称性，从而有助于对物理过程的理解和模拟。 PIC的命题可以在发现更广泛的物理场景中发现未透视的管理方程式中PDE发现的实际应用。
Data-driven discovery of PDEs has made tremendous progress recently, and many canonical PDEs have been discovered successfully for proof-of-concept. However, determining the most proper PDE without prior references remains challenging in terms of practical applications. In this work, a physics-informed information criterion (PIC) is proposed to measure the parsimony and precision of the discovered PDE synthetically. The proposed PIC achieves state-of-the-art robustness to highly noisy and sparse data on seven canonical PDEs from different physical scenes, which confirms its ability to handle difficult situations. The PIC is also employed to discover unrevealed macroscale governing equations from microscopic simulation data in an actual physical scene. The results show that the discovered macroscale PDE is precise and parsimonious, and satisfies underlying symmetries, which facilitates understanding and simulation of the physical process. The proposition of PIC enables practical applications of PDE discovery in discovering unrevealed governing equations in broader physical scenes.
