Regressão simbólica em redes complexas

Abstract

Discovering the equations that govern a system from observations is fundamental in several areas of science, as it enables both understanding its properties and predicting future behavior. Recently, machine learning techniques based on symbolic regression have emerged as an automated alternative for this task, with the advantage of not requiring prior domain knowledge to effectively describe dynamical systems, although they may benefit from such knowledge to refine the obtained equations. This study aims to develop a new methodology for the analysis and inference of complex phenomena by analyzing and comparing the performance of multiple symbolic regression algorithms in identifying epidemic dynamical systems across different propagation environments. Traditionally, temporal dynamics analyses rely on sequentially organized linear data, an approach that is limited when studying systems in which interconnections among elements and recurrent interactions decisively influence their evolution. To overcome this limitation, the research was structured into two approaches: the first using data from homogeneous environments and the second from heterogeneous environments. In both cases, symbolic regression algorithms were applied, using the fit obtained from Random Forest models as a reference. The effectiveness of the methods was evaluated through descriptive analysis and the application of the Wilcoxon test to assess significant differences between real and estimated dynamics. In the second approach, inferential statistical analysis was included to investigate the influence of network topology on the accuracy of the regressors. The results show that some algorithms, such as SINDy, SR, and MultKAN, demonstrated a high capacity to reconstruct the underlying dynamics in both approaches, with SR achieving the best performance among them. However, no significant effects of network topology were detected on algorithm performance, except with respect to R2, which was already expected. These findings indicate that the learned equations proved to be generalizable to the scenarios described here, regardless of the structural characteristics of the propagation environment, thereby supporting their potential implementation in real-world public health settings.