使用物理信息的神经网络的整数和分数顺序流行病学模型的识别性和可预测性
Ehsan Kharazmi1, Min Cai1,2, Xiaoning Zheng1,3
1Division of Applied Mathematics, Brown University, Providence, RI, USA.
Nature computational science
|January 13, 2024
概括
基于物理学的神经网络 (PINNs) 在流行病学模型中确定了依赖时间的参数和分数运算符. 这种方法通过推断未知的动态和参数来准确预测COVID-19的传播.
科学领域:
- 流行病学 流行病学
- 计算数学 计算数学 计算数学
- 机器学习 机器学习
背景情况:
- 流行病学模型对于了解疾病传播至关重要.
- 传统模型经常与时间变化的参数和复杂的动力学作斗争.
- 基于物理学的神经网络 (PINNs) 提供了一种解决这些局限性的新方法.
研究的目的:
- 在流行病学模型中应用PINN来识别时间依赖的参数和小数差异运算符.
- 分析易受感染移除 (SIR) 模型的变异,包括分数顺序和时间延迟模型.
- 调查这些模型在现实世界流行病预测中的可识别性和不确定性量化.
主要方法:
- 利用PINNs分析流行病学模型,包括SIR变异.
- 将分数顺序和时间延迟动态纳入模型.
- 使用神经网络表示依赖时间的参数和分数顺序.
- 将该方法应用于来自纽约市,罗德岛,密歇根州和意大利的COVID-19数据.
主要成果:
- 成功推断了整数顺序和时间延迟模型的时间依赖参数.
- 对于分数微分模型来说,确定了依赖时间的分数导数订单.
- 证明了PINNs能够同时推断出未知的参数和未观察到的动态的能力.
- 与神经网络预测和控制措施相关的量化不确定性.
结论:
- PINNs为增强流行病学建模提供了一个强大的框架.
- 该方法允许识别复杂的,时间变化的动态和参数.
- 通过改进模型识别能力和不确定性量化,可以准确预测COVID-19等大流行病的传播.
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