arXiv:2505.21879cs.SCcs.AI2025-05

用预训练符号回归模型,高效发现复杂网络中的科学规律。

Symbolic Foundation Regressor on Complex Networks

  • 基于预训练符号回归,压缩多变量数据并生成可解释方程
  • 在复杂网络上推理效率提升3倍,预测精度高
  • 适合需理解机制的物理、生物、流行病学研究者

在科学研究中,我们不仅关注预测,更关心预测背后的可解释模型。数据驱动的机器学习技术能大幅缩短传统手动发现科学定律的耗时过程,帮助揭示现代科学的核心问题。本文提出一种预训练符号基础回归模型,能有效压缩具有大量相互作用变量的复杂数据,并生成可解释的物理表达式。该模型在非网络符号回归、复杂网络符号回归及跨领域网络动态推断(包括物理、生物化学、生态学与流行病学)中均经过严格测试。结果表明,方程推断效率比基线方法高出三倍,同时保持高预测准确率。进一步应用于全球疫情爆发数据,成功揭示更具直观性的传播机制,实现最优数据拟合。本模型将预训练符号回归的应用范围扩展至复杂网络,为揭示复杂现象变化背后的隐藏机理提供了基础性解决方案,增强可解释性,激发更多科学发现。

原文摘要 · Abstract (English)

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.

符号回归复杂网络可解释模型科学发现

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