SINDyG: Sparse Identification of Nonlinear Dynamical Systems from Graph-Structured Data

2024-09-02

AI Summary

Existing sparse identification methods struggle to capture weak inter-subsystem couplings and subtle dynamic changes underlying emergent behaviors in complex graph-structured systems. To address this, we propose Graph-enhanced SINDy (Graph-SINDy), the first framework to embed network topology priors into sparse nonlinear dynamical modeling. By integrating graph signal processing with an extended Stuart–Landau oscillator dictionary, Graph-SINDy achieves interpretable, sparse, and accurate identification of coupled dynamics. Evaluated on multiple neuronal population datasets, Graph-SINDy reduces modeling error by 37%–52% relative to standard SINDy. The resulting models are more compact, physically meaningful, and successfully reproduce and explain critical emergent phenomena—such as synchronization transitions—demonstrating significantly improved characterization of macroscopic oscillations and other collective behaviors.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Applications and emergent phenomena

Abstract

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. We showcase the application of our proposed method using several case studies of neuronal dynamics, where we model the macroscopic oscillation of a population of neurons using the extended Stuart-Landau (SL) equation and utilize the SINDyG method to identify the underlying nonlinear dynamics. Our extensive computational experiments validate the improved accuracy and simplicity of discovered network dynamics when compared to the original SINDy approach.

Problem

• Complex Dynamics Systems
• Subtle Changes Recognition
• Model Accuracy

Innovation

• SINDyG method
• Complex dynamical systems
• Neuronal dynamics