Identifying partial differential equations (PDEs) from data is crucial for understanding the governing mechanisms of natural phenomena, yet it remains a challenging task. We present an extension to the ARGOS framework, ARGOS-RAL, which leverages sparse regression with the recurrent adaptive lasso to identify PDEs from limited prior knowledge automatically. Our method automates calculating partial derivatives, constructing a candidate library, and estimating a sparse model. We rigorously evaluate the performance of ARGOS-RAL in identifying canonical PDEs under various noise levels and sample sizes, demonstrating its robustness in handling noisy and non-uniformly distributed data. We also test the algorithm's performance on datasets consisting solely of random noise to simulate scenarios with severely compromised data quality. Our results show that ARGOS-RAL effectively and reliably identifies the underlying PDEs from data, outperforming the sequential threshold ridge regression method in most cases. We highlight the potential of combining statistical methods, machine learning, and dynamical systems theory to automatically discover governing equations from collected data, streamlining the scientific modeling process.

ARGOS-RAL利用稀疏回归结合循环自适应lasso从有限先验知识中自动识别偏微分方程(PDEs)，其性能在各种噪声水平和样本量下得到了严格评估，展示了在处理噪声和非均匀分布的数据方面的稳健性。通过将统计方法、机器学习和动力系统理论相结合，ARGOS-RAL在大多数情况下效果优于顺序阈值岭回归方法，突显了从收集到的数据中自动发现控制方程的潜力，从而简化科学建模过程。

动态系统中的偏微分方程自动发现