Discovering Governing equations from Graph-Structured Data by Sparse Identification of Nonlinear Dynamical Systems

• Published in: arXiv.org 2024-09
• Main Authors: Mohammad Amin Basiri, Khanmohammadi, Sina
• Format: Article
• Language: English
• Subjects: Climate models; Dynamic models; Dynamical systems; Identification methods; Machine learning; Nonlinear systems; Parameter identification; Regression models; Structured data; Subsystems
• ISSN: 2331-8422

The combination of machine learning (ML) and sparsity-promoting techniques is enabling direct extraction of governing equations from data, revolutionizing computational modeling in diverse fields of science and engineering. The discovered dynamical models could be used to address challenges in climate science, neuroscience, ecology, finance, epidemiology, and beyond. However, most existing sparse identification methods for discovering dynamical systems treat the whole system as one without considering the interactions between subsystems. As a result, such models are not able to capture small changes in the emergent system behavior. To address this issue, we developed a new method called Sparse Identification of Nonlinear Dynamical Systems from Graph-structured data (SINDyG), which incorporates the network structure into sparse regression to identify model parameters that explain the underlying network dynamics. SINDyG discovers the governing equations of network dynamics while offering improvements in accuracy and model simplicity.