Finite Expression Method for Learning Dynamics on Complex Networks

Abstract: Complex network data pervades various real-world domains, including physical, technological, and biological systems. Despite the prevalence of such data, predicting trends and understanding behavioral patterns in complex systems remains challenging due to poorly understood underlying mechanisms. While data-driven methods have made strides 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. To address these challenges, we introduce a novel approach called the Finite Expression Method (FEX) and its fast algorithm for this learning problem 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. Our extensive numerical experiments demonstrate that FEX excels in accurately identifying dynamics across diverse network topologies and dynamic behaviors.