A variety of approaches using compartmental models have been used to study the COVID-19 pandemic and the usage of machine learning methods with these models has had particularly notable success. We present here an approach toward analyzing accessible data on Covid-19's U.S. development using a variation of the "Physics Informed Neural Networks" (PINN) which is capable of using the knowledge of the model to aid learning. We illustrate the challenges of using the standard PINN approach, then how with appropriate and novel modifications to the loss function the network can perform well even in our case of incomplete information. Aspects of identifiability of the model parameters are also assessed, as well as methods of denoising available data using a wavelet transform. Finally, we discuss the capability of the neural network methodology to work with models of varying parameter values, as well as a concrete application in estimating how effectively cases are being tested for in a population, providing a ranking of U.S. states by means of their respective testing.

翻译：我们在此提出一种分析可获取的Covid-19美国发展数据的方法,使用“物理知情神经网络”(PINN)的变异方法,能够利用该模型的知识帮助学习。我们介绍了使用标准PINN方法的挑战,然后说明了如何适当和新颖地修改网络的损失功能,即使我们的信息不完整,也可以很好地改进网络的损失功能。还评估了模型参数的可识别性,以及利用波盘变换去现有数据的方法。最后,我们讨论了神经网络方法与不同参数值模型合作的能力,以及具体应用来估计在人口中测试案例的有效性,通过各自的测试提供美国各州的排名。