Automating the discovery of partial differential equations in dynamical systems

Li, Weizhen; Carvalho, Rui

Abstract

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.

Citation

Li, W., & Carvalho, R. (2024). Automating the discovery of partial differential equations in dynamical systems. Machine Learning: Science and Technology, 5(3), Article 035046. https://doi.org/10.1088/2632-2153/ad682f

• Journal Article Type: Article
• Acceptance Date: Jul 26, 2024
• Online Publication Date: Aug 14, 2024
• Publication Date: Sep 1, 2024
• Deposit Date: Aug 20, 2024
• Publicly Available Date: Aug 20, 2024
• Journal: Machine Learning: Science and Technology
• Print ISSN: 2632-2153
• Electronic ISSN: 2632-2153
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 5
• Issue: 3
• Article Number: 035046
• DOI: https://doi.org/10.1088/2632-2153/ad682f
• Keywords: partial differential equations, nonlinear dynamics, machine learning, sparse regression, system identification
• Public URL: https://durham-repository.worktribe.com/output/2760998