A Modified PINN Approach for Identifiable Compartmental Models in Epidemiology with Application to COVID-19

Many approaches using compartmental models have been used to study the COVID-19 pandemic, with machine learning methods applied to these models having particularly notable success. We consider the Susceptible-Infected-Confirmed-Recovered-Deceased (SICRD) compartmental model, with the goal of estimating the unknown infected compartment I, and several unknown parameters. We apply a variation of a "Physics Informed Neural Network" (PINN), which uses knowledge of the system to aid learning. First, we ensure estimation is possible by verifying the model's identifiability. Then, we propose a wavelet transform to process data for the network training. Finally, our central result is a novel modification of the PINN's loss function to reduce the number of simultaneously considered unknowns. We find that our modified network is capable of stable, efficient, and accurate estimation, while the unmodified network consistently yields incorrect values. The modified network is also shown to be efficient enough to be applied to a model with time-varying parameters. We present an application of our model results for ranking states by their estimated relative testing efficiency. Our findings suggest the effectiveness of our modified PINN network, especially in the case of multiple unknown variables.