Year: 2024
Type: preprint
Abstract: Complex network data is prevalent in various real-world domains, including physical, technological, and biological systems. Despite this prevalence, predicting trends and understanding behavioral patterns in complex systems remain challenging due to poorly understood underlying mechanisms. While data-driven methods have advanced in uncovering governing equations from time series data, efforts to extract physical laws from network data are limited and often struggle with incomplete or noisy data. Additionally, they suffer from computational costs on network data, making it difficult to scale to real-world networks. To address these challenges, we introduce a novel approach called the Finite Expression Method (FEX) and its fast algorithm for learning dynamics on complex networks. FEX represents dynamics on complex networks using binary trees composed of finite mathematical operators. The nodes within these trees are trained through a combinatorial optimization process guided by reinforcement learning techniques. This unique configuration allows FEX to capture complex dynamics with minimal prior knowledge of the system and a small dictionary of mathematical operators. We also integrate a fast, stochastic algorithm into FEX, reducing the computational complexity from $O(N^2)$ to $O(N)$. Our extensive numerical experiments demonstrate that FEX excels in accurately identifying dynamics across diverse network topologies and dynamic behaviors.
Source: arXiv (Cornell University)
Authors: Song, Zezheng, Wang, Chunmei, Yang, Haizhao
Institutions: University of Maryland, College Park, University of Florida
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4390722740