从微观动力学鲁棒发现粗粒度连续介质方程

中文摘要 AI 辅助

直接从时空数据发现控制偏微分方程（PDE）已成为理解复杂系统动力学的强大工具。本研究将PDE-SINDy应用于著名的相分离系统，考察其性能如何依赖可用数据量、函数库规模以及噪声的存在。结果表明，方程发现的准确性强烈依赖于可用数据量：尽管有限数据即可识别正确方程，但若干虚假项也会获得有限的选择概率；随着数据量增加，这些虚假项会被逐步抑制，从而实现对控制方程更鲁棒的识别。相反，增大函数库规模会对方程发现的效率产生不利影响。此外，针对Glauber自旋翻转伊辛模型，研究显示选择概率揭示了具有不同复杂度层级的方程体系；足够严格的选择阈值可恢复出类似Model-A的动力学方程，该方程能准确复现相分离与畴生长的动力学及统计特征。

英文摘要

Data-driven discovery of governing equations from spatiotemporal data offers a promising route to obtaining coarse-grained descriptions of complex dynamical systems. Here, we investigate the performance of PDE-SINDy for discovering phase-ordering dynamics using the Allen--Cahn equation as a benchmark and the Ising model with Glauber spin-flip dynamics as a microscopic system. We systematically analyze the effects of data availability, size of the candidate library, and noise on the efficiency of the equation discovery. We find that stability-selection PDE-SINDy can robustly identify the relevant terms in the governing dynamics even under limited or noisy data, while the recovered coefficient values are substantially more sensitive to these factors. We further show that enlarging the candidate library can strongly affect both term identification and coefficient recovery. Incorporating library bagging with stability selection reduces this sensitivity and improves the efficiency of equation discovery. For the Glauber spin flip Ising model dynamics, the resulting coarse-grained equation reproduces the characteristic phase-separation and coarsening dynamics of the underlying microscopic system. Overall, our results demonstrate the potential of PDE-SINDy for phase-ordering systems while highlighting the importance of carefully assessing the factors that influence the efficiency of equation discovery.

发表机构

• Indian Institute of Technology (BHU) Varanasi（印度理工学院（瓦拉纳西）BHU校区）

机构由 AI 辅助整理，请以论文原文为准。

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15 pages, 15 figures