将科尔莫戈罗夫-阿诺德网络与普通微分方程集成为高效,可解释和强大的深度学习:传染病流行病学作为一个案例研究
Kexin Ma1, Xu Lu2, Nicola Luigi Bragazzi3
1School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, People's Republic of China.
Infectious Disease Modelling
|January 8, 2026
概括
本研究介绍了与普通微分方程 (KAN-UDE) 集成的Kolmogorov-Arnold网络 (KAN),以实现流行病学中的高效和可解释的深度学习. KAN-UDE模型显示出卓越的性能,并重建机械模型,改善疾病趋势预测.
科学领域:
- 计算科学是一种计算科学.
- 流行病学 流行病学
- 机器学习是机器学习.
背景情况:
- 万能微分方程 (UDEs) 提供了一个深度学习的框架,用微分方程来进行深度学习.
- 现有的UDE经常使用多层感知子,这可能缺乏可解释性.
- 流行病学建模需要准确和强大的疾病动态预测.
研究的目的:
- 将科尔莫戈罗夫-阿诺德网络 (KAN) 与UDE (KAN-UDE) 集成,以提高深度学习.
- 评估KAN-UDE在模拟新兴传染病流行病学的表现.
- 评估KAN-UDE的解释性和机械重建能力.
主要方法:
- 通过将KAN与普通微分方程结合起来,开发了KAN-UDE.
- 在流行病学时间序列数据上训练KAN-UDE模型.
- 基于多层感知子的KAN-UDE性能与传统的UDE性能进行比较.
- 将KAN-UDE模型重建成完全机械模型 (RMM).
主要成果:
- 与基于MLP的UDEs相比,KAN-UDE表现出明显改善的装配性能,并迅速减少损失.
- 模型准确地重建了非线性函数,即使使用了部分和稀疏的时间序列数据.
- KAN-UDE通过使RMM重建成为RMM,促进了可解释的学习.
- 虽然KAN-UDE对现实数据随机性的稳定性较低,但RMM提供了强大而准确的长期流行病趋势预测.
结论:
- KAN-UDE为微分方程提供了一种高效和可解释的深度学习方法.
- 该框架显示了流行病学建模的前景,特别是在重建机制理解方面.
- 来自KAN-UDE的重建机械模型 (RMM) 提供了强大的长期预测,尽管数据噪声.
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