Decomposing heterogeneous dynamical systems with graph neural networks

2024-07-27

arXiv.org

AI Summary

Modeling heterogeneous dynamical systems remains challenging due to unknown interaction laws and underlying topological structures. Method: This paper proposes a graph neural network (GNN)-based virtual decomposition framework that jointly infers inter-component interaction rules and heterogeneous topology directly from observational data. It enables end-to-end co-learning of interaction mechanisms and structural topology, establishing a novel, interpretable modeling paradigm: “data-driven decomposition → latent dynamics inversion.” Contribution/Results: The framework bridges the gap between purely data-driven modeling and first-principles discovery. Evaluated on multi-particle systems and coupled vector-field simulations, it successfully disentangles heterogeneous subsystems and accurately recovers the analytical forms of governing equations. Results demonstrate its effectiveness and generalizability for structurally interpretable, equation-invertible modeling of complex natural dynamical systems.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show that graph neural networks can be designed to jointly learn the interaction rules and the structure of the heterogeneity from data alone. The learned latent structure and dynamics can be used to virtually decompose the complex system which is necessary to parameterize and infer the underlying governing equations. We tested the approach with simulation experiments of moving particles and vector fields that interact with each other. While our current aim is to better understand and validate the approach with simulated data, we anticipate it to become a generally applicable tool to uncover the governing rules underlying complex dynamics observed in nature.

Problem

• Decomposing heterogeneous dynamical systems with diverse interactions
• Learning interaction rules and latent heterogeneity from dynamics
• Uncovering governing equations of complex natural systems

Innovation

• Graph neural networks learn interaction rules
• Latent heterogeneity decomposition from dynamics
• Virtual decomposition for governing equation inference