Calibration of Time-Dependent Parameters in Compartmental Epidemiological Models Using Physics-Informed Neural Networks: An Application to the Italian Covid-19 Pandemic

We propose to use Physics-Informed Neural Networks (PINNs) to track the temporal changes in the state variables and transmission rate of an epidemic based on the SIR model equation and infectious data. PINNs consider both the information from data (typically uncertain) and the governing equations of the system. We develop a reduced-split approach for the implementation of PINNs that: • splits the training first on the epidemiological data, and then on the residual of the system equations; • reduces the number of functions that are approximated and eliminates any redundant term in the loss. Our results show that this implementation of PINNs outperforms the standard joint approach in terms of accuracy (up to one order of magnitude) and computational times (speed up of 20%).