使用柯尔莫哥洛夫 - 阿诺德网络和傅里叶级数估计随时间变化的新冠疫情参数
EPI-KAN: A Method For Estimating and Forecasting Time-Dependent COVID-19 Parameters
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中文总结 AI 辅助
研究利用柯尔莫哥洛夫 - 阿诺德网络（KAN）和傅里叶级数（KAN - F），通过物理信息神经网络（PINN）或Epi - DNN最小化目标损失函数，估计新冠疫情随时间变化的参数，用三国数据验证方法有效且效率较高。
中文摘要 AI 辅助
我们介绍了一种估计新冠疫情随时间变化参数的新方法。这些参数基于SIRD房室微分方程，包括传播率β(t)、恢复率γ(t)和死亡率μ(t)。该方法利用新型柯尔莫哥洛夫 - 阿诺德网络（KAN），即一种人工神经网络，其激活函数用傅里叶级数表示，简称KAN - F。我们定义了三个KAN - F函数分别模拟真实参数。目标损失函数需通过物理信息神经网络（PINN）或Epi - DNN最小化。利用东南亚三个国家的数据估计参数，在特定时期，使用Epi - DNN和KAN - F能以不错的准确率和相对效率估计出β(t)、γ(t)和μ(t)。印尼训练4316步，新加坡8408步，马来西亚8000步。三国的三个函数均采用2个隐藏层的相同KAN - F架构，分别有8个输入神经元、17个第一隐藏层神经元、35个第二隐藏层神经元和1个输出神经元，每个激活函数的傅里叶项数为30。
英文摘要
We introduce EPI-KAN, a novel method for estimating COVID-19 time-varying parameters. EPI-KAN uses historical epidemiological data, Physics-Informed Neural Network (PINN), and the novel Kolmogorov-Arnold Network (KAN). The method harnesses the novel Kolmogorov-Arnold Network (KAN), which is a type of artificial neural network. For the KAN in this paper, we learn activation functions that are represented using Fourier series, hence we abbreviate as KAN-F. In this study, we estimate parameters in the context of an SIRD compartmental differential equations. The time-dependent parameters are the transmission rate $β(t)$, recovery rate $γ(t)$, and mortality rate $μ(t)$. We define three KAN-F functions $\widehatβ$, $\widehatγ$, $\widehatμ$ that model the true parameters $β(t)$, $γ(t)$, $μ(t)$, respectively. We test two model architectures for the KAN-F: the first has 8 input variables consisting of $S$, $I$, $R$, $D$, and their numerical gradients at any time $t$, while the second has 4 input variables excluding the numerical gradients. The objective loss function that has to be minimized is subject to Physics-Informed Neural Network (PINN). Using historical data of COVID-19 from three South-East Asian countries: Indonesia, Singapore, and Malaysia, we are able to estimate $β(t)$, $γ(t)$, and $μ(t)$ on each country with decent accuracy and efficiency. The time period of choice coincides with the period where SARS-CoV-2 Delta variant (B.1.617.2) was dominant. In addition to estimating the rates during the training period, we also predict transmission rates over 30 days during forecast period. We found that the output of KAN-F over the forecast period can give good predictions if we scale the output by a factor of 17\% for Indonesia and 30\% for Singapore and Malaysia.
