Automating the Discovery of Partial Differential Equations in Dynamical Systems
This work addresses the challenge of automating PDE discovery from data for scientific modeling, though it is incremental as an extension to an existing framework.
The authors tackled the problem of automatically identifying partial differential equations (PDEs) from noisy and limited data in dynamical systems, presenting ARGOS-RAL, an extension of the ARGOS framework that uses sparse regression with recurrent adaptive lasso. Their results show it effectively and reliably identifies underlying PDEs, outperforming sequential threshold ridge regression in most cases.
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.