Kharazmi Ehsan, Cai Min, Zheng Xiaoning, Zhang Zhen, Lin Guang, Karniadakis George Em
Division of Applied Mathematics, Brown University, Providence, RI, USA.
Department of Mathematics, Shanghai University, Shanghai, China.
Nat Comput Sci. 2021 Nov;1(11):744-753. doi: 10.1038/s43588-021-00158-0. Epub 2021 Nov 22.
We analyze a plurality of epidemiological models through the lens of physics-informed neural networks (PINNs) that enable us to identify time-dependent parameters and data-driven fractional differential operators. In particular, we consider several variations of the classical susceptible-infectious-removed (SIR) model by introducing more compartments and fractional-order and time-delay models. We report the results for the spread of COVID-19 in New York City, Rhode Island and Michigan states and Italy, by simultaneously inferring the unknown parameters and the unobserved dynamics. For integer-order and time-delay models, we fit the available data by identifying time-dependent parameters, which are represented by neural networks. In contrast, for fractional differential models, we fit the data by determining different time-dependent derivative orders for each compartment, which we represent by neural networks. We investigate the structural and practical identifiability of these unknown functions for different datasets, and quantify the uncertainty associated with neural networks and with control measures in forecasting the pandemic.
我们通过物理信息神经网络（PINNs）来分析多个流行病学模型，这使我们能够识别随时间变化的参数和数据驱动的分数阶微分算子。具体而言，我们通过引入更多分区以及分数阶和时滞模型，考虑了经典的易感-感染-康复（SIR）模型的几种变体。我们通过同时推断未知参数和未观测到的动态，报告了新冠病毒在纽约市、罗德岛州、密歇根州以及意大利传播的结果。对于整数阶和时滞模型，我们通过识别由神经网络表示的随时间变化的参数来拟合可用数据。相比之下，对于分数阶微分模型，我们通过为每个分区确定不同的随时间变化的导数阶数来拟合数据，这些导数阶数由神经网络表示。我们研究了这些未知函数对于不同数据集的结构和实际可识别性，并量化了在预测大流行时与神经网络和控制措施相关的不确定性。
