用科学机器学习建模病毒传播，提升预测精度并揭示抑制机制。
Understanding Malware Propagation Dynamics through Scientific Machine Learning
- 结合物理规律与神经网络，用通用微分方程建模病毒传播。
- 相比传统和纯神经模型，预测误差降低44%，且保持可解释性。
- 适合网络安全研究者、威胁情报分析及防御系统设计人员。
准确建模恶意软件传播对设计有效网络安全防御至关重要，尤其针对实时演化的自适应威胁。传统流行病学模型与近期神经方法虽有基础价值，但常无法充分捕捉真实网络中的非线性反馈机制。本文采用科学机器学习，评估三类方法：经典常微分方程（ODE）、通用微分方程（UDE）与神经微分方程（Neural ODE）。基于Code Red蠕虫爆发数据，结果显示UDE方法相较传统与神经基线预测误差降低44%，同时保持可解释性。我们提出符号恢复方法，将学习到的神经反馈转化为显式数学表达式，揭示了网络饱和、安全响应与变种演化等抑制机制。结果表明，混合物理信息模型可超越纯解析与纯神经方法，在预测精度与动态理解上均更优，支持早期预警系统、高效应急响应与精准防御干预的开发。
原文摘要 · Abstract (English)
Accurately modeling malware propagation is essential for designing effective cybersecurity defenses, particularly against adaptive threats that evolve in real time. While traditional epidemiological models and recent neural approaches offer useful foundations, they often fail to fully capture the nonlinear feedback mechanisms present in real-world networks. In this work, we apply scientific machine learning to malware modeling by evaluating three approaches: classical Ordinary Differential Equations (ODEs), Universal Differential Equations (UDEs), and Neural ODEs. Using data from the Code Red worm outbreak, we show that the UDE approach substantially reduces prediction error compared to both traditional and neural baselines by 44%, while preserving interpretability. We introduce a symbolic recovery method that transforms the learned neural feedback into explicit mathematical expressions, revealing suppression mechanisms such as network saturation, security response, and malware variant evolution. Our results demonstrate that hybrid physics-informed models can outperform both purely analytical and purely neural approaches, offering improved predictive accuracy and deeper insight into the dynamics of malware spread. These findings support the development of early warning systems, efficient outbreak response strategies, and targeted cyber defense interventions.
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