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.

翻译：从数据中识别偏微分方程（PDEs）对于理解自然现象的支配机制至关重要，但这仍然是一项具有挑战性的任务。我们提出了ARGOS框架的扩展版本——ARGOS-RAL，该方法利用稀疏回归与递归自适应套索（recurrent adaptive lasso），在有限先验知识下自动识别PDEs。我们的方法实现了偏导数的自动计算、候选库的构建以及稀疏模型的估计。我们严格评估了ARGOS-RAL在不同噪声水平和样本量下识别标准PDEs的性能，证明了其在处理含噪及非均匀分布数据时的鲁棒性。我们还测试了该算法在仅含随机噪声的数据集上的性能，以模拟数据质量严重受损的场景。结果表明，ARGOS-RAL能够有效且可靠地从数据中识别潜在的PDEs，在大多数情况下优于序贯阈值岭回归方法。我们强调了将统计方法、机器学习与动力系统理论相结合，以从采集数据中自动发现支配方程的潜力，从而简化科学建模过程。