Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion
This work addresses the challenge of practical PDE discovery in broader physical scenes, enabling applications where prior references are unavailable.
The authors tackled the problem of discovering partial differential equations (PDEs) from highly noisy and sparse data by proposing a physics-informed information criterion (PIC) to measure parsimony and precision, achieving state-of-the-art robustness on seven canonical PDEs and successfully discovering unrevealed macroscale governing equations from microscopic simulation data.
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.