Symbolic Foundation Regressor on Complex Networks

TL;DR

This paper introduces a pre-trained symbolic foundation regressor that efficiently compresses complex data, produces interpretable models, and uncovers underlying scientific laws across various domains, especially on complex networks.

Contribution

The work extends pre-trained symbolic regression to complex networks, improving equation inference efficiency and interpretability in scientific data analysis.

Findings

Threefold improvement in inference efficiency over baselines

Effective modeling of network dynamics in multiple scientific domains

Successful discovery of intuitive laws from epidemic data

Abstract

In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline the complex and time-consuming traditional manual process of discovering scientific laws, helping us gain insights into fundamental issues in modern science. In this work, we introduce a pre-trained symbolic foundation regressor that can effectively compress complex data with numerous interacting variables while producing interpretable physical representations. Our model has been rigorously tested on non-network symbolic regression, symbolic regression on complex networks, and the inference of network dynamics across various domains, including physics, biochemistry, ecology, and epidemiology. The results indicate a remarkable improvement in equation inference efficiency, being three times more effective than baseline approaches while maintaining accurate predictions. Furthermore, we apply our model to uncover more intuitive laws of interaction transmission from global epidemic outbreak data, achieving optimal data fitting. This model extends the application boundary of pre-trained symbolic regression models to complex networks, and we believe it provides a foundational solution for revealing the hidden mechanisms behind changes in complex phenomena, enhancing interpretability, and inspiring further scientific discoveries.