从微观数据中稳健发现粗粒化方程，揭示噪声与数据量的影响
Robust Discovery of Coarse-Grained Continuum Equations from Microscopic Dynamics
- 用PDE-SINDy方法从时空数据中自动发现系统演化方程
- 数据越多，错误项越被抑制，方程识别更可靠
- 设定严格阈值可恢复出准确的模型A类动力学方程
从时空数据中直接发现支配复杂系统演化的偏微分方程（PDE）已成为理解其动态的重要工具。本文将PDE-SINDy应用于经典的相分离系统，研究其性能如何受可用数据量、函数库规模和噪声影响。结果表明，方程发现的准确性强烈依赖于数据量：尽管少量数据下可识别正确方程，但多个虚假项仍具有有限选择概率；随着数据增加，这些虚假项逐步被抑制，方程识别趋于稳健。相反，扩大函数库会降低发现效率。对于Glauber自旋翻转伊辛模型，选择概率揭示了不同复杂度方程的层级结构。设定足够严格的筛选阈值后，可恢复出准确再现相分离与畴生长动态及统计特征的模型A类动力学方程。
原文摘要 · Abstract (English)
The discovery of governing partial differential equations (PDEs) directly from spatiotemporal data has emerged as a powerful tool for understanding the dynamics of complex systems. In this work, we apply PDE-SINDy to well-known phase-separating systems and examine how its performance depends on the amount of available data, the size of the function library, and the presence of noise. Our results show that the accuracy of equation discovery depends strongly on the amount of available data. Although the correct equation can be identified with limited data, several spurious terms also acquire finite selection probabilities. As the amount of data increases, these spurious terms are progressively suppressed, leading to a more robust identification of the governing equation. In contrast, increasing the size of the function library adversely affects the efficiency of equation discovery. Further, for the Glauber spin-flip Ising model, we show that the selection probabilities reveal a hierarchy of equations with varying levels of complexity. A sufficiently stringent selection threshold recovers a Model-A-like dynamical equation that accurately reproduces the dynamical and statistical features of phase separation and domain growth.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。